A variety of mechanisms for deuteron production in relativistic nuclear collisions are considered. These include the coalescence model, the sudden approximation model, and the static thermal model. A new model based on time dependent perturbation theory is presented. A solution of the rate equations for a hydrodynamically expanding fireball suggests that chemical equilibrium might be achieved in central collisions. Emphasis is placed on the physical assumptions of the various models, their limitations, and their subtly different predictions. Of some importance is the effect of impact parameter averaging which, when written in terms of the usual power law relationship, introduces the necessity for measuring various two particle correlation functions to check the self-consistency of these models. NUCLEAR REACTIONS Relativistic heavy ions, models for deuteron production p-n correlations.