  This paper surveys the recent advances in the interactions between symbolic
dynamics and C*-algebras. We explain how conjugacies and orbit equivalences of
both two-sided (invertible) and one-sided (noninvertible) symbolic systems may
be encoded into C*-algebras, and how the dynamical systems can be recovered
from structure-preserving *-isomorphisms of C*-algebras. We have included many
illustrative examples as well as open problems.
