Langrangian statistical (Monte Carlo) simulations of the mean and fluctuating concentration fields due to turbulent dispersion are critically reviewed. Attention has been restricted to work in which particle trajectories are modeled directly, which in effect means simulations based on the Langevin equation (or in finite difference form, Markov-chains) and its generalization. The material covered has been selected and presented so as to achieve an orderly progression from simple to more complex turbulent flows. At present this field involves many heuristic modeling assumptions and an attempt is made to justify some of these by appeal to special and limiting cases.