A deterministic modeling approach – as the one explained in Chap. 2 assumes to deal with systems isolated from any source of noise, or randomness, that could spoil model predictions. In classical physics this approximation is generally valid. Biological systems, however, are intrinsically noisy, which makes deterministic models inappropriate to simulate, at least, certain kinds of synthetic gene circuits. The stochastic simulation (or Gillespie) algorithm is a purely computational approach to calculate the temporal evolution of biological systems. In principle, it may give a more realistic description of gene circuit dynamics. However, it becomes computationally too demanding if applied to large synthetic networks. In this Chapter, we will explain the theoretical foundations, working, and recent improvements of this algorithm. Moreover, we will discuss under which conditions a deterministic model can provide faithful predictions, despite the complexity of the system, and when, in contrast, stochastic simulations are preferable.