diff --git a/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConstrainedDelaunayTriangulationCellBase_3.h b/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConstrainedDelaunayTriangulationCellBase_3.h
index 530ec67c984..c9567fd4427 100644
--- a/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConstrainedDelaunayTriangulationCellBase_3.h
+++ b/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConstrainedDelaunayTriangulationCellBase_3.h
@@ -17,4 +17,29 @@ the `CGAL::Constrained_Delaunay_triangulation_3` class template.
 */
 class ConstrainedDelaunayTriangulationCellBase_3 {
 public:
+  bool is_marked() const;
+  bool is_marked(CDT_3_cell_marker m);
+  void set_mark(CDT_3_cell_marker m);
+  void clear_mark(CDT_3_cell_marker m);
+  void clear_marks();
+
+  bool is_facet_constrained(int i);
+
+  template <typename Facet_handle>
+  void set_facet_constraint(int i, CDT_3_face_index face_id,
+                            Facet_handle facet_2d);
+
+  CDT_3_face_index face_constraint_index(int i);
+
+  template <typename CDT_2>
+  auto face_2 (const CDT_2& cdt, int i);
+};
+
+/// @brief Enum type for cell markers.
+enum class CDT_3_cell_marker {
+  CLEAR = 0,
+  IN_REGION = 1,
+  VISITED = 1,
+  ON_REGION_BOUNDARY = 2,
+  nb_of_markers
 };
diff --git a/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConstrainedDelaunayTriangulationVertexBase_3.h b/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConstrainedDelaunayTriangulationVertexBase_3.h
index c79c468e6c6..635a9204dc1 100644
--- a/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConstrainedDelaunayTriangulationVertexBase_3.h
+++ b/Constrained_triangulation_3/doc/Constrained_triangulation_3/Concepts/ConstrainedDelaunayTriangulationVertexBase_3.h
@@ -1,3 +1,8 @@
+/*! @brief a signed integral type
+ * \relates ConstrainedDelaunayTriangulationVertexBase_3
+ */
+using CDT_3_face_index = int;
+
 /*!
 \cgalConcept
 
@@ -17,4 +22,48 @@ the `CGAL::Constrained_Delaunay_triangulation_3` class template.
 */
 class ConstrainedDelaunayTriangulationVertexBase_3 {
 public:
+  void set_on_constraint(auto constraint_id);
+
+  int number_of_incident_constraints() const;
+
+  void set_mark(CDT_3_vertex_marker marker);
+
+  void clear_marks();
+
+  void clear_mark(CDT_3_vertex_marker marker);
+
+  bool is_marked(CDT_3_vertex_marker marker) const;
+
+  bool is_marked() const;
+
+  template<typename Triangulation>
+  auto constraint_id(const Triangulation&) const;
+
+  void set_Steiner_vertex_in_face(CDT_3_face_index face_index);
+
+  CDT_3_face_index face_index() const;
+
+  CDT_3_vertex_type vertex_type() const;
+  void set_vertex_type(CDT_3_vertex_type type);
+  bool is_Steiner_vertex_on_edge() const;
+  bool is_Steiner_vertex_in_face() const;
 };
+
+namespace CGAL {
+/// \enum CDT_3_vertex_marker
+/// @brief Enum type for vertex markers
+/// \addtogroup PkgCT_3_enums
+enum class CDT_3_vertex_marker {
+  CLEAR = 0,     ///< No marker
+  REGION_BORDER, ///< On the border of the region
+  REGION_INSIDE, ///< Inside the region
+  CAVITY,        ///< In the cavity
+  CAVITY_ABOVE,  ///< In the cavity above
+  CAVITY_BELOW,  ///< In the cavity below
+  nb_of_markers  ///< Number of markers
+};
+
+/// \enum CDT_3_vertex_type
+/// \addtogroup PkgCT_3_enums
+enum class CDT_3_vertex_type { FREE, CORNER, STEINER_ON_EDGE, STEINER_IN_FACE };
+}
diff --git a/Constrained_triangulation_3/doc/Constrained_triangulation_3/PackageDescription.txt b/Constrained_triangulation_3/doc/Constrained_triangulation_3/PackageDescription.txt
index fdce18f529b..d0d2f45cdb5 100644
--- a/Constrained_triangulation_3/doc/Constrained_triangulation_3/PackageDescription.txt
+++ b/Constrained_triangulation_3/doc/Constrained_triangulation_3/PackageDescription.txt
@@ -1,5 +1,7 @@
 /// \defgroup PkgCT_3Ref 3D Constrained Triangulations Reference
 
+/// \defgroup PkgCT_3_enums Enumerations
+
 /*!
 \addtogroup PkgCT_3Ref
 \cgalPkgDescriptionBegin{3D Constrained Triangulations,PkgCT_3}