This paper describes the state of the art in reservoir simulation for the nonexpert, focusing primarily on advances that have occured since a similar paper was published by Coats, K. H. in 1982. A history of simulation is given first, followed by a brief and simple review of the simulation process. Advances in simulation technology are presented, highlighting those in reservoir description and simulation of naturally fractured reservoirs, hydraulic fracturing, and horizontal wells. The fracture of reservoir simulation is described last.