  We review a self-consistent scheme for modelling trapped weakly-interacting
quantum gases at temperatures where the condensate coexists with a significant
thermal cloud. This method has been applied to atomic gases by Zaremba, Nikuni,
and Griffin, and is often referred to as ZNG. It describes both
mean-field-dominated and hydrodynamic regimes, except at very low temperatures
or in the regime of large fluctuations. Condensate dynamics are described by a
dissipative Gross-Pitaevskii equation (or the corresponding quantum
hydrodynamic equation with a source term), while the non-condensate evolution
is represented by a quantum Boltzmann equation, which additionally includes
collisional processes which transfer atoms between these two subsystems. In the
mean-field-dominated regime collisions are treated perturbatively and the full
distribution function is needed to describe the thermal cloud, while in the
hydrodynamic regime the system is parametrised in terms of a set of local
variables. Applications to finite temperature induced damping of collective
modes and vortices in the mean-field-dominated regime are presented.
