Gromov's theory of hyperbolic groups has had a big impact on combinatorial group theory and has connections with such branches of mathematics as differential geometry, representation theory, ergodic theory and dynamical systems. This book elaborates on some of Gromov's ideas on hyperbolic spaces and hyperbolic groups in relation to symbolic dynamics. Particular attention is paid to the dynamical system defined by the action of a hyperbolic group on its boundary. The boundary is most often chaotic, both as a topological space and as a dynamical system, and a description of this boundary and its action is given in terms of subshifts of finite type. The book is self-contained and includes two introductory chapters, one on Gromov's hyperbolic geometry and the other on symbolic dynamics.