The behavior of automata in labyrinths

We present a survey of more than 80 papers, written over the last 20 years, on the behavior of systems of automata in labyrinths. We focus on fundamental concepts, problems, accomplishments, methods for problem solving, and open problems. In a number of cases the basic theorems are presented in a stronger form than the formulations of the authors. The paper also contains new results on the problem of traversing labyrinths by automata.