  In this paper, we propose a general framework for designing numerical schemes
that have both well-balanced (WB) and asymptotic preserving (AP) properties,
for various kinds of kinetic models. We are interested in two different
parameter regimes, 1) When the ratio between the mean free path and the
characteristic macroscopic length $\epsilon$ tends to zero, the density can be
described by (advection) diffusion type (linear or nonlinear) macroscopic
models; 2) When $\epsilon$ = O(1), the models behave like hyperbolic equations
with source terms and we are interested in their steady states. We apply the
framework to three different kinetic models: neutron transport equation and its
diffusion limit, the transport equation for chemotaxis and its Keller-Segel
limit, and grey radiative transfer equation and its nonlinear diffusion limit.
Numerical examples are given to demonstrate the properties of the schemes.
