  In this review we consider those processes in condensed matter that involve
the irreversible flow of energy between electrons and nuclei that follows from
a system being taken out of equilibrium. We survey some of the more important
experimental phenomena associated with these processes, followed by a number of
theoretical techniques for studying them. The techniques considered are those
that can be applied to systems containing many non-equivalent atoms. They
include both perturbative approaches (Fermi's Golden Rule, and non-equilibrium
Green's functions) and molecular dynamics based (the Ehrenfest approximation,
surface hopping, semi-classical gaussian wavefunction methods and correlated
electron-ion dynamics). These methods are described and characterised, with
indications of their relative merits.
