This work considers the stability and stabilization of switched descriptor systems in discrete-time domain. First, the concept of regularity, causality are formulated for such systems. Next, the stability under arbitrary switching signals are investigated. The common Lyapunov functional method and the switched Lyapunov functional method are extended from the regular switched linear systems to the switched descriptor case. Some sufficient conditions are established under which the system is regular, causal and asymptotically stable under arbitrary switching signal, and, if a set of matrix inequalities is solvable, a switched state feedback controller can be designed to stabilize the system under arbitrary switching signal.