This talk will survey some recent advances in the development of
transition regime models from kinetic equations. The classes of
stationary-balance models and quasistationary-balance models will be
presented for linear kinetic equations. These models share elements
with both traditional moment closures and expansions. They also
include a natural framework for developing boundary conditions
Generalizations of these ideas to nonlinear kinetic settings include
entropy-based moment closures, and hierarchies of fluid dynamical
systems for the classical Boltzmann equation that dissipate entropy
and include dispersive terms with higher order space derivatives.