  We discuss Implicit-Explicit (IMEX) Runge Kutta methods which are
particularly adapted to stiff kinetic equations of Boltzmann type. We consider
both the case of easy invertible collision operators and the challenging case
of Boltzmann collision operators. We give sufficient conditions in order that
such methods are asymptotic preserving and asymptotically accurate. Their
monotonicity properties are also studied. In the case of the Boltzmann
operator, the methods are based on the introduction of a penalization technique
for the collision integral. This reformulation of the collision operator
permits to construct penalized IMEX schemes which work uniformly for a wide
range of relaxation times avoiding the expensive implicit resolution of the
collision operator. Finally we show some numerical results which confirm the
theoretical analysis.
