  This talk summarises what is currently understood about the phenomenon that
has come to be known as {\it chaotic mixing}. The first part presents a concise
statement as to what chaotic mixing actually is, and then explains why it
should be important in galactic dynamics. The second discusses in detail what
is currently known, describing the manifestations of chaotic mixing both for
flows in time-independent Hamiltonian systems and for systems subjected to
comparatively weak time-dependent perturbations. The third part discusses what
one might expect if one were to allow for a strongly time-dependent potential,
including possible implications for violent relaxation.
