In the previous three chapters, we studied the necessary optimality conditions and sufficient optimality conditions of the MPEC. This chapter discusses three general classes of iterative algorithms for computing a stationary point of an MPEC. The first class of algorithms is based on a penalty interior point approach (PIPA); the second class of algorithms is based on an implicit programming approach. The third class of algorithms is of the Newton type for solving MPEC, based on the piecewise programming formulation. For the latter algorithms, some conditions pertaining to the relaxed nonlinear program introduced at the end of Subsection 4.3.1 turn out to provide useful conditions for their convergence. In essence, the interior point approach is applicable to MPECs where the lower-level problems possess certain generalized monotonicity properties; the second approach relies on the implicit program formulation of the MPEC; in particular, the SCOC assumption introduced in Subsection 4.2.7 will play an important role in this approach. In both approaches, we establish that any accumulation point of the iterates produced by the algorithms must be a stationary point of MPEC provided that the point satisfies a strict complementarity assumption. The third class of algorithms is an extension of some locally convergent Newton methods for solving smooth nonlinear programs extended to a piecewise smooth setting; thus these algorithms are locally convergent in the sense that a closeness assumption is required on the initial iterate in order to guarantee convergence. Like their smooth counterpart, the piecewise smooth Newton algorithms have superlinear (and even quadratic) rates of convergence under mild assumptions. The chapter ends with a section that reports some preliminary computational results with a MATLAB implementation of PIPA; see Section 6.5.