A growing realization of the importance of stochasticity in cell and molecular processes has stimulated the need for statistical models that incorporate intrinsic (and extrinsic) variability. In this chapter we consider stochastic kinetic models of reaction networks leading to a Markov jump process representation of a system of interest. Traditionally, the stochastic model is characterized by a chemical master equation. While the intractability of such models can preclude a direct analysis, simulation can be straightforward and may present the only practical approach to gaining insight into a system's dynamics. We review exact simulation procedures before considering some efficient approximate alternatives.