Computer simulation of multiphase flows has grown dramatically in the last decade. Problems as diverse as the Brownian motion of small colloidal particles or single DNA molecules, the theology of dense suspensions and emulsions, and the dynamics of bubbly liquids have been addressed by dynamic simulation. This paper traces the development of the methodologies used to simulate multiphase, particulate systems. A central feature in these problems is to properly account for the hydrodynamic interactions among particles, which has been accomplished rigorously and successfully in the case of small particle Reynolds numbers and in the limit of inviscid flow at high Reynolds numbers. Examples showing how hydrodynamic forces influence suspension structure and determine macroscopic behavior for viscous suspensions are given.