In the monograph we present some results of the work we have done in the theory of classical Homogeneous structures (HS; HS–models) and their appendices during 1969–2013, in truth with considerable pauses. Meantime, during the present book along with the given term its well-known Anglo–lingual equivalent «Cellular automata – CA» is used too. These results at present form a rather essential constituent of the HS–problematics. In particular, we have researched such problems as the nonconstructability problem in HS, the problem of decomposition of global transition functions in HS, extremal constructive opportunities, parallel formal grammars and languages defined by HS, complexity of finite configurations and global transition functions in HS, simulation problem in classical HS, the computer simulation of HS, some applied aspects of the HS, etc. At present, the HS–problematics is a rather well developed independent sphere of the mathematical cybernetics which has considerable field of numerous appendices. At that, with the equal right the HS–problematics can be considered as a component of such fields as the discrete parallel dynamic systems, discrete mathematics, cybernetics, complex systems and some others. In our viewpoint, the book will present an indubitable interest for students, post–graduates and persons working for doctor's degree of the appropriate faculties of universities and colleges, first of all, of naturally scientific level along with teachers in such disciplines as discrete mathematics, cybernetics, automata theory, computer science, theoretical biology, mathematical and physical modelling, computer technique, and a lot of others.