diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/algebraic_segments.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/algebraic_segments.cpp
index a546f9c16ae..95eb729bb66 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/algebraic_segments.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/algebraic_segments.cpp
@@ -2,6 +2,7 @@
 // Constructing an arrangement of algebraic segments.
 
 #include <iostream>
+#include <cassert>
 #include <CGAL/config.h>
 
 #if (!CGAL_USE_CORE) && (!CGAL_USE_LEDA) && (!(CGAL_USE_GMP && CGAL_USE_MPFI))
@@ -52,7 +53,7 @@ int main() {
   std::vector<X_monotone_curve> segs;
   for(size_t i = 0; i < pre_segs.size(); ++i) {
     auto* curr_p = boost::get<X_monotone_curve>(&pre_segs[i]);
-    CGAL_assertion(curr_p);
+    assert(curr_p);
     segs.push_back(*curr_p);
   }
   // Construct an ellipse (C2) with the equation 2*x^2+5*y^2-7=0.
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/conics.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/conics.cpp
index f01501c054a..a8688f55a98 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/conics.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/conics.cpp
@@ -29,7 +29,7 @@ int main() {
   // with (-3, 4) and (4, 3) as its endpoints. We want the arc to be
   // clockwise-oriented, so it passes through (0, 5) as well.
   Conic_arc c4(Rat_point(-3, 4), Rat_point(0, 5), Rat_point(4, 3));
-  CGAL_assertion(c4.is_valid());
+
   insert(arr, c4);
 
   // Insert a full unit circle (C5) that is centered at (0, 4).
@@ -46,7 +46,7 @@ int main() {
               0, 0, 0, 0, 1, 3,                  // the line: y = -3.
               Point(1.41, -2),                   // approximation of the target.
               0, 0, 0, 0, 1, 2);                 // the line: y = -2.
-  CGAL_assertion(c6.is_valid());
+
   insert(arr, c6);
 
   // Insert the right half of the circle centered at (4, 2.5) whose radius
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/dual_lines.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/dual_lines.cpp
index b6b4304c1a0..36a5cbb3b5b 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/dual_lines.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/dual_lines.cpp
@@ -3,6 +3,7 @@
 // using the arrangement of the dual lines.
 
 #include <cstdlib>
+#include <cassert>
 
 #include "arr_linear.h"
 #include "read_objects.h"
@@ -74,7 +75,7 @@ int main(int argc, char* argv[]) {
       break;
     }
   }
-  CGAL_assertion(found_collinear);
+  assert(found_collinear);
 
   return (0);
 }
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/edge_manipulation_curve_history.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/edge_manipulation_curve_history.cpp
index 59c36abf614..e89d8b57d89 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/edge_manipulation_curve_history.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/edge_manipulation_curve_history.cpp
@@ -46,7 +46,6 @@ int main() {
   const Point q{_7_halves, 7};
   Point_location::result_type obj = pl.locate(q);
   auto* e = boost::get<Arr_with_hist::Halfedge_const_handle>(&obj);
-  CGAL_assertion(e);
 
   // Split the edge e to two edges e1 and e2;
   auto e1 = arr.split_edge(arr.non_const_handle(*e), q);
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/face_extension_overlay.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/face_extension_overlay.cpp
index c5fbb593f25..7eda7deea85 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/face_extension_overlay.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/face_extension_overlay.cpp
@@ -1,6 +1,8 @@
 //! \file examples/Arrangement_on_surface_2/face_extension_overlay.cpp
 // A face overlay of two arrangements with extended face records.
 
+#include <cassert>
+
 #include <CGAL/basic.h>
 #include <CGAL/Arr_overlay_2.h>
 #include <CGAL/Arr_default_overlay_traits.h>
@@ -21,7 +23,8 @@ int main() {
   insert_non_intersecting_curve(arr1, Segment(Point(6, 2), Point(6, 6)));
   insert_non_intersecting_curve(arr1, Segment(Point(6, 6), Point(2, 6)));
   insert_non_intersecting_curve(arr1, Segment(Point(2, 6), Point(2, 2)));
-  CGAL_assertion(arr1.number_of_faces() == 2);
+  // 2 because the bounded and the unbounded one
+  assert(arr1.number_of_faces() == 2);
 
   // Mark just the bounded face.
   for (auto fit = arr1.faces_begin(); fit != arr1.faces_end(); ++fit)
@@ -33,7 +36,6 @@ int main() {
   insert_non_intersecting_curve(arr2, Segment(Point(7, 4), Point(4, 7)));
   insert_non_intersecting_curve(arr2, Segment(Point(4, 7), Point(1, 4)));
   insert_non_intersecting_curve(arr2, Segment(Point(1, 4), Point(4, 1)));
-  CGAL_assertion(arr2.number_of_faces() == 2);
 
   for (auto fit = arr2.faces_begin(); fit != arr2.faces_end(); ++fit)
     fit->set_data(fit != arr2.unbounded_face());    // mark the bounded face.
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/incremental_insertion.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/incremental_insertion.cpp
index 7f6e63e1661..51112be6c50 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/incremental_insertion.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/incremental_insertion.cpp
@@ -33,7 +33,7 @@ int main() {
   Point q(4, 1);
   auto obj = pl.locate(q);
   auto* f = boost::get<Arrangement::Face_const_handle>(&obj);
-  CGAL_assertion(f != nullptr);
+
   std::cout << "The query point (" << q << ") is located in: ";
   print_face<Arrangement>(*f);
 
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/overlay_color.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/overlay_color.cpp
index 0a1e106681d..6cb7f17f477 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/overlay_color.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/overlay_color.cpp
@@ -1,6 +1,8 @@
 //! \file examples/Arrangement_on_surface_2/overlay_color.cpp
 // The overlay of two arrangement with extended dcel structures
 
+#include <cassert>
+
 #include <CGAL/basic.h>
 #include <CGAL/Arr_extended_dcel.h>
 #include <CGAL/Arr_overlay_2.h>
@@ -25,7 +27,7 @@ int main() {
   insert(arr1, Segment(Point(0, 0), Point(0, 4)));
   insert(arr1, Segment(Point(2, 0), Point(2, 4)));
   insert(arr1, Segment(Point(4, 0), Point(4, 4)));
-  CGAL_assertion(arr1.number_of_faces() == 5);
+  assert(arr1.number_of_faces() == 5);
   for (auto vit = arr1.vertices_begin(); vit != arr1.vertices_end(); ++vit)
     vit->set_data(vcol1);
   for (auto hit = arr1.halfedges_begin(); hit != arr1.halfedges_end(); ++hit)
@@ -41,7 +43,7 @@ int main() {
   insert(arr2, Segment(Point(0, 0), Point(0, 6)));
   insert(arr2, Segment(Point(3, 0), Point(3, 6)));
   insert(arr2, Segment(Point(6, 0), Point(6, 6)));
-  CGAL_assertion(arr2.number_of_faces() == 5);
+  assert(arr2.number_of_faces() == 5);
   for (auto vit = arr2.vertices_begin(); vit != arr2.vertices_end(); ++vit)
     vit->set_data(vcol2);
   for (auto hit = arr2.halfedges_begin(); hit != arr2.halfedges_end(); ++hit)
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polycurve_bezier.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polycurve_bezier.cpp
index 020320acb89..287fd51786a 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polycurve_bezier.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/polycurve_bezier.cpp
@@ -59,7 +59,6 @@ int main() {
     std::vector<Make_x_monotone_result> obj_vector;
     bezier_traits.make_x_monotone_2_object()(B, std::back_inserter(obj_vector));
     auto* x_seg_p = boost::get<Bezier_x_monotone_curve>(&obj_vector[0]);
-    CGAL_assertion(x_seg_p);
     x_curves.push_back(*x_seg_p);
   }
 
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/spherical_degenerate_sweep.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/spherical_degenerate_sweep.cpp
index 4646b0cda36..8c6f46dfeb6 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/spherical_degenerate_sweep.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/spherical_degenerate_sweep.cpp
@@ -5,6 +5,7 @@
 // #define CGAL_ARRANGEMENT_ON_SURFACE_INSERT_VERBOSE 1
 // #define CGAL_ARR_CONSTRUCTION_SL_VISITOR_VERBOSE 1
 
+#include <cassert>
 #include <vector>
 
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
@@ -57,26 +58,26 @@ int main() {
   X_monotone_curve_2 xcv_sp1 = ctr_xcv(sp, p1);
   X_monotone_curve_2 xcv_sp2 = ctr_xcv(sp, p2);
   X_monotone_curve_2 xcv_sp3 = ctr_xcv(sp, p3);
-  CGAL_assertion(xcv_sp1.is_vertical());
-  CGAL_assertion(xcv_sp2.is_vertical());
-  CGAL_assertion(xcv_sp3.is_vertical());
+  assert(xcv_sp1.is_vertical());
+  assert(xcv_sp2.is_vertical());
+  assert(xcv_sp3.is_vertical());
   xcvs.push_back(xcv_sp1);      // 0
   xcvs.push_back(xcv_sp2);      // 1
   xcvs.push_back(xcv_sp3);      // 2
 
   X_monotone_curve_2 xcv_12 = ctr_xcv(p1, p2);
   X_monotone_curve_2 xcv_23 = ctr_xcv(p2, p3);
-  CGAL_assertion(!xcv_12.is_vertical());
-  CGAL_assertion(!xcv_23.is_vertical());
+  assert(!xcv_12.is_vertical());
+  assert(!xcv_23.is_vertical());
   xcvs.push_back(xcv_12);       // 3
   xcvs.push_back(xcv_23);       // 4
 
   X_monotone_curve_2 xcv_np1 = ctr_xcv(np, p1);
   X_monotone_curve_2 xcv_np2 = ctr_xcv(np, p2);
   X_monotone_curve_2 xcv_np3 = ctr_xcv(np, p3);
-  CGAL_assertion(xcv_np1.is_vertical());
-  CGAL_assertion(xcv_np2.is_vertical());
-  CGAL_assertion(xcv_np3.is_vertical());
+  assert(xcv_np1.is_vertical());
+  assert(xcv_np2.is_vertical());
+  assert(xcv_np3.is_vertical());
   xcvs.push_back(xcv_np1);      // 5
   xcvs.push_back(xcv_np2);      // 6
   xcvs.push_back(xcv_np3);      // 7
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unb_planar_vertical_decomposition.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unb_planar_vertical_decomposition.cpp
index 72dc3469703..831e0e44395 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unb_planar_vertical_decomposition.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unb_planar_vertical_decomposition.cpp
@@ -45,7 +45,6 @@ int main() {
       if (vh) std::cout << '(' << (*vh)->point() << ')';
       else {
         auto* hh = boost::get<Halfedge_const_handle>(&*(curr.first));
-        CGAL_assertion(hh);
         if (! (*hh)->is_fictitious())
           std::cout << '[' << (*hh)->curve() << ']';
         else std::cout << "NONE";
@@ -59,7 +58,6 @@ int main() {
       if (vh) std::cout << '(' << (*vh)->point() << ")\n";
       else {
         auto* hh = boost::get<Halfedge_const_handle>(&*(curr.second));
-        CGAL_assertion(hh);
         if (! (*hh)->is_fictitious())
           std::cout << '[' << (*hh)->curve() << "]\n";
         else std::cout << "NONE\n";
diff --git a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp
index 159d66a6184..7de9d0981d6 100644
--- a/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp
+++ b/Arrangement_on_surface_2/examples/Arrangement_on_surface_2/unbounded_non_intersecting.cpp
@@ -2,6 +2,8 @@
 // Constructing an arrangement of unbounded linear objects using the insertion
 // function for non-intersecting curves.
 
+#include <cassert>
+
 #include "arr_linear.h"
 #include "arr_print.h"
 
@@ -13,7 +15,7 @@ int main() {
   X_monotone_curve c1 = Line(Point(-1, 0), Point(1, 0));
   arr.insert_in_face_interior(c1, arr.unbounded_face());
   Vertex_handle v = insert_point(arr, Point(0,0));
-  CGAL_assertion(! v->is_at_open_boundary());
+  assert(! v->is_at_open_boundary());
 
   // Add two more rays using the specialized insertion functions.
   arr.insert_from_right_vertex(Ray(Point(0, 0), Point(-1, 1)), v); // c2
diff --git a/Boolean_set_operations_2/examples/Boolean_set_operations_2/circle_segment.cpp b/Boolean_set_operations_2/examples/Boolean_set_operations_2/circle_segment.cpp
index 523f1961907..7cf3ec3dc7b 100644
--- a/Boolean_set_operations_2/examples/Boolean_set_operations_2/circle_segment.cpp
+++ b/Boolean_set_operations_2/examples/Boolean_set_operations_2/circle_segment.cpp
@@ -8,6 +8,7 @@
 #include <CGAL/Lazy_exact_nt.h>
 
 #include <list>
+#include <cassert>
 
 typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
 typedef Kernel::Point_2                                   Point_2;
@@ -28,7 +29,7 @@ Polygon_2 construct_polygon (const Circle_2& circle)
   Curve_2 curve (circle);
   std::list<CGAL::Object>  objects;
   traits.make_x_monotone_2_object() (curve, std::back_inserter(objects));
-  CGAL_assertion (objects.size() == 2);
+  assert(objects.size() == 2);
 
   // Construct the polygon.
   Polygon_2 pgn;
diff --git a/Boolean_set_operations_2/examples/Boolean_set_operations_2/set_union.cpp b/Boolean_set_operations_2/examples/Boolean_set_operations_2/set_union.cpp
index a6d2e2e3dd6..cecacc9a107 100644
--- a/Boolean_set_operations_2/examples/Boolean_set_operations_2/set_union.cpp
+++ b/Boolean_set_operations_2/examples/Boolean_set_operations_2/set_union.cpp
@@ -10,6 +10,7 @@
 #include <list>
 #include <cstdlib>
 #include <cmath>
+#include <cassert>
 
 typedef CGAL::Exact_predicates_exact_constructions_kernel Kernel;
 typedef Kernel::Point_2                                   Point_2;
@@ -29,7 +30,7 @@ Polygon_2 construct_polygon (const Circle_2& circle)
   Curve_2 curve (circle);
   std::list<CGAL::Object> objects;
   traits.make_x_monotone_2_object() (curve, std::back_inserter(objects));
-  CGAL_assertion (objects.size() == 2);
+  assert(objects.size() == 2);
 
   // Construct the polygon.
   Polygon_2 pgn;
diff --git a/Envelope_2/examples/Envelope_2/envelope_circles.cpp b/Envelope_2/examples/Envelope_2/envelope_circles.cpp
index daae2157203..94da9077706 100644
--- a/Envelope_2/examples/Envelope_2/envelope_circles.cpp
+++ b/Envelope_2/examples/Envelope_2/envelope_circles.cpp
@@ -8,6 +8,7 @@
 #include <CGAL/Arrangement_2.h>
 #include <CGAL/Envelope_diagram_1.h>
 #include <CGAL/envelope_2.h>
+#include <cassert>
 
 typedef CGAL::Exact_rational                          Number_type;
 typedef CGAL::Cartesian<Number_type>                  Kernel;
@@ -42,7 +43,7 @@ void print_diagram (const Diagram_1& diag)
 
     e = v->right();
   }
-  CGAL_assertion (e->is_empty());
+  assert(e->is_empty());
   std::cout << "Edge: [empty]" << std::endl;
 
   return;
diff --git a/Envelope_2/examples/Envelope_2/envelope_segments.cpp b/Envelope_2/examples/Envelope_2/envelope_segments.cpp
index 751d4feb501..e3cd1d9fa99 100644
--- a/Envelope_2/examples/Envelope_2/envelope_segments.cpp
+++ b/Envelope_2/examples/Envelope_2/envelope_segments.cpp
@@ -10,6 +10,7 @@
 
 #include <list>
 #include <iostream>
+#include <cassert>
 
 typedef CGAL::Exact_rational                            Number_type;
 typedef CGAL::Cartesian<Number_type>                    Kernel;
@@ -74,7 +75,7 @@ int main ()
 
     e = v->right();
   }
-  CGAL_assertion (e->is_empty());
+  assert(e->is_empty());
   std::cout << "Edge: [empty]" << std::endl;
 
   return (0);
diff --git a/Minkowski_sum_2/examples/Minkowski_sum_2/bops_linear.h b/Minkowski_sum_2/examples/Minkowski_sum_2/bops_linear.h
index 65668686580..d6e57c0eef1 100644
--- a/Minkowski_sum_2/examples/Minkowski_sum_2/bops_linear.h
+++ b/Minkowski_sum_2/examples/Minkowski_sum_2/bops_linear.h
@@ -2,6 +2,7 @@
 #define BOPS_LINEAR_H
 
 #include <list>
+#include <cassert>
 
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Boolean_set_operations_2.h>
diff --git a/Minkowski_sum_2/examples/Minkowski_sum_2/sum_triangle_square.cpp b/Minkowski_sum_2/examples/Minkowski_sum_2/sum_triangle_square.cpp
index 5923d1e5fdf..de46f19e9e4 100644
--- a/Minkowski_sum_2/examples/Minkowski_sum_2/sum_triangle_square.cpp
+++ b/Minkowski_sum_2/examples/Minkowski_sum_2/sum_triangle_square.cpp
@@ -21,7 +21,7 @@ int main()
 
   // Compute the Minkowski sum.
   Polygon_with_holes_2  sum = CGAL::minkowski_sum_2(P, Q);
-  CGAL_assertion(sum.number_of_holes() == 0);
+  assert(sum.number_of_holes() == 0);
   std::cout << "P (+) Q = " << sum.outer_boundary() << std::endl;
   return 0;
 }
diff --git a/Surface_sweep_2/examples/Surface_sweep_2/plane_sweep.cpp b/Surface_sweep_2/examples/Surface_sweep_2/plane_sweep.cpp
index d6d2fbbdfa8..28f894cd8bf 100644
--- a/Surface_sweep_2/examples/Surface_sweep_2/plane_sweep.cpp
+++ b/Surface_sweep_2/examples/Surface_sweep_2/plane_sweep.cpp
@@ -1,7 +1,8 @@
-//! \file examples/Arrangement_on_surface_2/plane_sweep.cpp
+//! \file examples/Surface_sweep_2/plane_sweep.cpp
 // Computing intersection points among curves using the surface-sweep alg.
 
 #include <list>
+#include <cassert>
 
 #include <CGAL/Exact_predicates_exact_constructions_kernel.h>
 #include <CGAL/Arr_segment_traits_2.h>
@@ -39,7 +40,7 @@ int main()
   std::cout << "Found " << sub_segs.size()
             << " interior-disjoint sub-segments." << std::endl;
 
-  CGAL_assertion(CGAL::do_curves_intersect (segments, segments + 4));
+  assert(CGAL::do_curves_intersect (segments, segments + 4));
 
   return 0;
 }