We describe the results of molecular simulation approaches to the study of reactions in near- and supercritical fluids. For simplicity, we carry out the simulations in a pure Lennard-Jones fluid but with the molecules initially tagged as "unreacted". We quantify the reaction rate in terms of the rate constant, measured either (a) by counting all collisions between pairs of reactants or (b) by tagging each colliding pair as "reacted", monitoring the concentration of "unreacted" molecules with time, and carrying out standard kinetic analyses. At low densities, both rate constants are identical to the kinetic theory result; at high density, only the reaction-based rate constant gives the physical result that the rate constant varies inversely with density (diffusion limitation). At intermediate density, there is a crossover between the two behaviors. We also describe the dependence of each type of rate constant on the cybotactic diameter (represented by the collision diameter in this work) of the reacting molecules. At low density, where the two rate constants are the same, their dependence on the collision diameter is identical to that of the equilibrium radial distribution function; i.e. locally high solute-solute correlations can influence the rate constant dramatically. At high density, where diffusion limitation sets in, the dependence on the collision diameter can be predicted from Smoluchowski theory and the influence of high peaks in the solute-solute radial distribution function all but disappears. This explains why the high solute-solute pair correlations measured in previous simulations do not appear to be manifested in most reaction studies made to date in supercritical fluids.