diff --git a/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h b/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h
index 6fecb592a12..9e46877c7d5 100644
--- a/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h
+++ b/Algebraic_kernel_d/include/CGAL/Algebraic_kernel_d/Curve_analysis_2.h
@@ -890,7 +890,7 @@ private:
                 break;
             }
             default:{
-              CGAL_assertion(false); // !!! Never reached
+              CGAL_unreachable();
             }
             }
         }
diff --git a/Alpha_shapes_2/include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h b/Alpha_shapes_2/include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h
index 6d77e38f904..c2fa9ca8d71 100644
--- a/Alpha_shapes_2/include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h
+++ b/Alpha_shapes_2/include/CGAL/Alpha_shapes_2/internal/Lazy_alpha_nt_2.h
@@ -212,7 +212,7 @@ public:
         exact_ = Exact_squared_radius()( to_exact(*data().p0),to_exact(*data().p1),to_exact(*data().p2) );
         break;
       default:
-        CGAL_assertion(false);
+        CGAL_unreachable();
     }
   }
 
@@ -229,7 +229,7 @@ public:
         approx_ = Approx_squared_radius()( to_approx(*data().p0),to_approx(*data().p1),to_approx(*data().p2) );
         break;
       default:
-        CGAL_assertion(false);
+        CGAL_unreachable());
     }
   }
 
diff --git a/Alpha_shapes_3/include/CGAL/Alpha_shapes_3/internal/Lazy_alpha_nt_3.h b/Alpha_shapes_3/include/CGAL/Alpha_shapes_3/internal/Lazy_alpha_nt_3.h
index 219c307815a..6023edd8e8b 100644
--- a/Alpha_shapes_3/include/CGAL/Alpha_shapes_3/internal/Lazy_alpha_nt_3.h
+++ b/Alpha_shapes_3/include/CGAL/Alpha_shapes_3/internal/Lazy_alpha_nt_3.h
@@ -224,7 +224,7 @@ public:
         approx_ = Approx_squared_radius()( to_approx(*data().p0),to_approx(*data().p1),to_approx(*data().p2),to_approx(*data().p3) );
       break;
       default:
-        CGAL_assertion(false);
+        CGAL_unreachable();
     }
   }
 
diff --git a/Arrangement_on_surface_2/include/CGAL/Arr_point_location/Td_X_trapezoid.h b/Arrangement_on_surface_2/include/CGAL/Arr_point_location/Td_X_trapezoid.h
index 9904b170542..674db5583fe 100644
--- a/Arrangement_on_surface_2/include/CGAL/Arr_point_location/Td_X_trapezoid.h
+++ b/Arrangement_on_surface_2/include/CGAL/Arr_point_location/Td_X_trapezoid.h
@@ -605,10 +605,9 @@ public:
     case CGAL_TD_VERTEX:
       return TD_VERTEX;
     default:
-       CGAL_assertion(false);
-       return TD_TRAPEZOID;
-    }
+       CGAL_unreachable();
     }
+  }
 
   /*! Access trapezoid type flag. */
   CGAL_TD_INLINE unsigned char type_flag() const
diff --git a/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h b/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h
index 4256fd0dc17..f1e83b22b0b 100644
--- a/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h
+++ b/Cone_spanners_2/include/CGAL/Compute_cone_boundaries_2.h
@@ -91,10 +91,8 @@ public:
     DirectionOutputIterator operator()(const unsigned int cone_number,
                                        const Direction_2& initial_direction,
                                        DirectionOutputIterator result)  {
-        if (cone_number<2) {
-            std::cout << "The number of cones must be larger than 1!" << std::endl;
-            CGAL_assertion(false);
-        }
+
+        CGAL_assertion_msg(cone_number>1, "The number of cones must be larger than 1");
 
         *result++ = initial_direction;
 
diff --git a/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h b/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h
index 8f2b599f311..71b4f338dd4 100644
--- a/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h
+++ b/Cone_spanners_2/include/CGAL/Construct_yao_graph_2.h
@@ -93,10 +93,7 @@ public:
                           ): cone_number(k), cones_choice(cones_selected), rays(std::vector<Direction_2>(k))
 
     {
-        if (k<2) {
-            std::cout << "The number of cones must be larger than 1!" << std::endl;
-            CGAL_assertion(false);
-        }
+        CGAL_assertion_msg(k>1, "The number of cones must be larger than 1");
 
         /* Initialize a functor, specialization will happen here depending on the kernel type to
          compute the cone boundaries either exactly or inexactly */
diff --git a/Kinetic_space_partition/include/CGAL/KSP_3/Intersection_graph.h b/Kinetic_space_partition/include/CGAL/KSP_3/Intersection_graph.h
index e86d696bc0b..a8779480c0b 100644
--- a/Kinetic_space_partition/include/CGAL/KSP_3/Intersection_graph.h
+++ b/Kinetic_space_partition/include/CGAL/KSP_3/Intersection_graph.h
@@ -420,7 +420,7 @@ public:
   }
 
   void set_crossed(const Edge_descriptor& edge, std::size_t sp_idx) {
-    CGAL_assertion(false);
+    CGAL_assertion(false);  // AF:  I am surprised that after the assert we do something
     m_graph[edge].crossed.insert(sp_idx);
   }
 };
diff --git a/Lab/demo/Lab/Plugins/PCA/Affine_transform_plugin.cpp b/Lab/demo/Lab/Plugins/PCA/Affine_transform_plugin.cpp
index 0edc6f05f18..0231529e692 100644
--- a/Lab/demo/Lab/Plugins/PCA/Affine_transform_plugin.cpp
+++ b/Lab/demo/Lab/Plugins/PCA/Affine_transform_plugin.cpp
@@ -728,7 +728,7 @@ end()
       endPolygonMesh(transform_matrix);
     break;
     default:
-      CGAL_assertion(false);
+      CGAL_unreachable();
   }
 
   dockWidget->hide();
diff --git a/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h b/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
index c85b1476fb9..5303221a9f3 100644
--- a/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
+++ b/Linear_cell_complex/include/CGAL/CMap_linear_cell_complex_storages_with_index.h
@@ -191,12 +191,8 @@ namespace CGAL {
       // Allocate a dart for null_dart_descriptor
       assert(mdarts.empty()); // the compact container is empty
       Dart_index local_null_dart_descriptor = mdarts.emplace();
-      if(local_null_dart_descriptor!=0)
-      {
-        std::cerr<<"[ERROR] fatal in CMap_linear_cell_complex_storage_with_index::init_storage"
-                 <<std::endl;
-        CGAL_assertion(false);
-      }
+      CGAL_assertion_msg(local_null_dart_descriptor==0,
+                          "[ERROR] fatal in CMap_linear_cell_complex_storage_with_index::init_storage");
     }
 
     void clear_storage()
diff --git a/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h b/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h
index 74dbb09b2ca..9bb07ec9d5d 100644
--- a/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h
+++ b/Mesh_3/include/CGAL/Mesh_3/Lloyd_move.h
@@ -100,9 +100,7 @@ public:
         break;
       default:
         // Should not happen
-        CGAL_assertion(false);
-        return CGAL::NULL_VECTOR;
-        break;
+        CGAL_unreachable();
     }
 
     return CGAL::NULL_VECTOR;
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersect_triangle_and_segment_3.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersect_triangle_and_segment_3.h
index 652d0b09952..afc259d4eab 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersect_triangle_and_segment_3.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/internal/Corefinement/intersect_triangle_and_segment_3.h
@@ -126,8 +126,8 @@ intersection_type(
       // p sees the triangle in counterclockwise order
     return find_intersection(p,q,a,b,c,h_2,tm2,false,true);
 
-    default: // should not happen.
-      CGAL_assertion(false);
+    default:
+      CGAL_unreachable();
       return result_type(EMPTY,GT::null_halfedge(),false,false);
     }
   case NEGATIVE:
@@ -143,8 +143,8 @@ intersection_type(
       // q belongs to the triangle's supporting plane
       // p sees the triangle in clockwise order
       return find_intersection(q,p,a,b,c,h_2,tm2,false,true);
-    default: // should not happen.
-      CGAL_assertion(false);
+    default:
+      CGAL_unreachable();
       return result_type(EMPTY,GT::null_halfedge(),false,false);
     }
   case COPLANAR: // p belongs to the triangle's supporting plane
@@ -163,12 +163,12 @@ intersection_type(
         return result_type(COPLANAR_TRIANGLES,GT::null_halfedge(),true,true);
       return result_type(EMPTY,GT::null_halfedge(),true,true);
 
-    default: // should not happen.
-      CGAL_assertion(false);
+    default:
+      CGAL_unreachable();
       return result_type(EMPTY,GT::null_halfedge(),false,false);
     }
-  default: // should not happen.
-    CGAL_assertion(false);
+  default:.
+    CGAL_unreachable();
     return result_type(EMPTY,GT::null_halfedge(),false,false);
   }
 }
diff --git a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Two_vertices_parameterizer_3.h b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Two_vertices_parameterizer_3.h
index 17cfb22d3a7..f69fe5416e8 100644
--- a/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Two_vertices_parameterizer_3.h
+++ b/Surface_mesh_parameterization/include/CGAL/Surface_mesh_parameterization/Two_vertices_parameterizer_3.h
@@ -205,7 +205,7 @@ public:
       V1_max = zmax;
       break;
     default:
-      CGAL_assertion(false);
+      CGAL_unreachable();
     }
     switch (second_longest_axis)
     {
@@ -225,7 +225,7 @@ public:
       V2_max = zmax;
       break;
     default:
-      CGAL_assertion(false);
+      CGAL_unreachable();
     }
 
     // Project onto longest bounding box axes,
diff --git a/TDS_2/include/CGAL/Triangulation_data_structure_2.h b/TDS_2/include/CGAL/Triangulation_data_structure_2.h
index 7eb651ef407..0b7b5d70a5e 100644
--- a/TDS_2/include/CGAL/Triangulation_data_structure_2.h
+++ b/TDS_2/include/CGAL/Triangulation_data_structure_2.h
@@ -1118,7 +1118,7 @@ insert_dim_up(Vertex_handle w,  bool orient)
     }
     break;
   default:
-    CGAL_assertion(false);
+    CGAL_unreachable();
     break;  }
   return v;
 }
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
index fd9981c1426..37fa5328006 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/smooth_vertices.h
@@ -875,7 +875,7 @@ std::size_t smooth_vertices_on_surfaces(C3t3& c3t3,
               return CGAL::midpoint(s->source(), s->target());
             else
             {
-              CGAL_assertion(false);
+              CGAL_assertion(false);   AF:  So are we not completely sure?
               return std::nullopt;
             }
           };
diff --git a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_remeshing_helpers.h b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_remeshing_helpers.h
index 2e93f2f8335..c39c85f3111 100644
--- a/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_remeshing_helpers.h
+++ b/Tetrahedral_remeshing/include/CGAL/Tetrahedral_remeshing/internal/tetrahedral_remeshing_helpers.h
@@ -844,7 +844,7 @@ void set_index(typename C3t3::Vertex_handle v, const C3t3& c3t3)
   case -1://far points from concurrent Mesh_3
     break;
   default:
-    CGAL_assertion(false);
+    CGAL_unreachable();
   }
 }
 
diff --git a/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h b/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
index 714e9295b61..6988b39ce5b 100644
--- a/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Constrained_Delaunay_triangulation_2.h
@@ -489,7 +489,7 @@ public:
       pit = propagate_conflicts(p,fh,2,pit);
       return pit;
     }
-    CGAL_assertion(false);
+    CGAL_unreachable();
     return std::make_pair(fit,eit);
   }
 
diff --git a/Triangulation_2/include/CGAL/Triangulation_2.h b/Triangulation_2/include/CGAL/Triangulation_2.h
index 433ea5cb5af..a7c1b543062 100644
--- a/Triangulation_2/include/CGAL/Triangulation_2.h
+++ b/Triangulation_2/include/CGAL/Triangulation_2.h
@@ -1488,7 +1488,7 @@ insert(const Point& p, Locate_type lt, Face_handle loc, int li)
   case VERTEX:
     return loc->vertex(li);
   }
-  CGAL_assertion(false); // locate step failed
+  CGAL_unreachable(); // AF: The comment  "locate step failed" gives the idea that it may fail, but all cases are covered
   return Vertex_handle();
 }