Collectives of automata in labyrinths

The behaviour of automata in labyrinths is a rather new field of automata theory, but more than one hundred papers devoted to this topic have been published. In this paper, we consider the key notions, problems, achievements, methods to solve problems, and open problems related to an important direction of this field, the behaviour of collectives of automata in labyrinths. In a series of cases, we give base assertions in a more strong form and give a more general presentation than the authors of the corresponding papers do. New results are also contained in this survey.