Complex systems can display complex phenomena that are not easily described at a microscopic level using molecular dynamics simulation methods. Systems may be complex because some or all of their constituents are complex molecular species, such as polymers, large biomolecules, or other molecular aggregates. Such systems can exhibit the formation of patterns arising from segregation of constituents or nonequilibrium effects and molecular shape changes induced by flows and hydrodynamic interactions. Even when the constituents are simple molecular entities, turbulent fluid motions can exist over a range of length and time scales.Many of these phenomena have their origins in interactions at the molecular level but manifest themselves over mesoscopic and macroscopic space and time scales. These features make the direct simulation of such systems difficult because one must follow the motions of very large numbers of particles over very long times. These considerations have prompted the development of coarse-grain methods that simplify the dynamics or the system in different ways in order to be able to explore longer length and time scales. The use of mesoscopic dynamical descriptions dates from the foundations of nonequilibrium statistical mechanics. The Boltzmann equation [1] provides a field description on times greater than the time of a collision and the Langevin equation [2] replaces a molecular-level treatment of the solvent with a stochastic description of its properties.The impetus to develop new types of coarse-grain or mesoscopic simulation methods stems from the need to understand and compute the dynamical properties of large complex systems. The method of choice usually depends on the type of information that is desired. If properties that vary on very long distance and time scales are of interest, the nature of the dynamics can be altered, while still preserving essential features to provide a faithful representation of these properties. For example, fluid flows described by the Navier-Stokes equations will result from dynamical schemes that preserve the basic conservation laws of mass, momentum, and energy. The details of the molecular interactions may be unimportant for such applications. Some coarsegrain approaches constructed in this spirit, such as the lattice Boltzmann method [3] and direct simulation Monte Carlo [4], are based on the Boltzmann equation. In dissipative particle dynamics [5, 6], several atoms are grouped into simulation sites whose dynamics is governed by conservative and frictional 90 raymond kapral 92 raymond kapral