New generalizations of cellular automata CA are described. This survey contains recent results published in research journals, conference proceedings etc. Cellular automata had been considered in the restricted regions of space. In this work, we propose the concepts for modelling logical gates by propagation of the gliders of cellular automata in a bounded domain and consider special roles for collisions of gliders with walls and obstacles. Also, the general formulations and properties of cellular automata with the strong anticipatory property of cells (introduced by D. Dubois) are considered. Multivalued behaviour (hyperincursion) of solutions of such CA is described. This poses new research problems of computation theory related to the presumable multivaluedness of cellular automata with strong anticipation properties. Extending of classical automata, Turing machine and algorithms had been proposed. Also, some relations of such cellular automata and quantum mechanics are discussed. Applications of cellular automata can remind well-known processes in real life like football games; migration in science and higher education; epidemic spreading; and artificial life.