We consider the problem of controlling nonlinear systems which are modeled as a set of piecewise linear (PL) or affine systems using model predictive control (MPC). The paper reviews recent results on the analysis and control of PL systems, which can model a wide range of practically relevant nonlinear systems. Using techniques from the theory of linear matrix inequalities (LMIs), we develop a multiple model MPC technique involving a sequence of local state feedback matrices, which minimize an upper bound on the 'worst-case' objective function. The resulting problem, which utilizes a single quadratic Lyapunov function and multiple local state-feedback matrices, can be cast as a convex optimization problem involving LMIs. Several extensions of this technique involving approximating the local regions by ellipsoids or polytopes, and their respective advantages and disadvantages, are discussed.