Most of the research on the development of fully automatic unstructured mesh generators has been concentrated on various triangulation schemes. Their advantage lies in the fact that simplicial elements (triangles and tetrahedrons) are most suitable to discretize domains of arbitrary complexity, particularly when locally graded meshes are needed. In the past, a wide class of algorithms for generation of triangular and tetrahedral meshes has been established, among which three basic strategies - the tree-based approach, advancing front technique, and Delaunay triangulation - have proved particularly successful. Currently, the dominating activity is focused on the development of methods for generation of quadrilateral and hexahedral meshes. This effort is driven, first of all, by the fact that quadrilateral and hexahedral elements are much more popular in the engineering analysis community because of their favourable features from the computational point of view. Although a variety of approaches for generation of quadrilateral meshes has been developed so far, only few algorithms for generation of hexahedral meshes (which is algorithmically much more complex) have been established. Thus a fully automatic discretization of general 3D geometries into all-hexahedral meshes still remains an open issue and is the subject of further research.