  This review is devoted to dynamical systems in fields of $p$-adic numbers:
origin of $p$-adic dynamics in $p$-adic theoretical physics (string theory,
quantum mechanics and field theory, spin glasses), continuous dynamical systems
and discrete dynamical systems. The main attention is paid to discrete
dynamical systems - iterations of maps in the field of $p$-adic numbers (or
their algebraic extensions): conjugate maps, ergodicity, random dynamical
systems, behaviour of cycles, holomorphic dynamics. dynamical systems in finite
fields. We also discuss applications of $p$-adic discrete dynamical systems to
cognitive sciences and psychology.
