The most important concepts and methods used in studying the geometrical and topological properties of crystal structures are considered, and a critical analysis of their potentialities for state-of-the-art crystal chemistry is performed. A new stereoatomic model of crystal structure is suggested in which atoms and atom groups are represented by their Voronoi-Dirichlet polyhedra. The fundamental difference between this model and the known applications of the Voronoi-Dirichlet polyhedra to crystal-chemical analysis is in the use of a number of rules, principles, and procedures based on the physically justified correlation between the characteristics of the domain of influence of an atom in the structure and those of its Voronoi-Dirichlet polyhedron. Numerous examples demonstrate the universality of the stereoatomic model, which allows one to appreciably automate the crystal-chemical analysis of both individual compounds and entire classes of inorganic and coordination compounds.