  We review the current state of Cepheid modeling and discuss its dominant
deficiency, namely the use of time dependent mixing length. Notwithstanding,
Cepheid modeling has achieved some excellent successes, and we mention some of
the most recent ones. Discrepancies between observations and modeling appear
not so much in the gross properties of single mode Cepheids, but rather when
more subtle nonlinear effects are important, such as in double mode or even
triple mode pulsations. Finally we discuss what we consider the most important
challenges for the next decade. These are, first, realistic multi dimensional
modeling of convection in a pulsating environment, and second, the nonlinear
modeling of the nonradial pulsations that have been observed, and, relatedly,
of the Blazhko like phenomenon that has recently been observed in Cepheids.

Solar and Stellar Astrophysics