In multiblock reservoir simulation techniques, the reservoir model is divided into a number of subdomains or blocks. In our current implementation, these blocks are locally structured but globally unstructured. This representation enables the modeling of geometrically complex reservoir features such as fault surfaces and nonconventional wells while avoiding many of the complications of fully unstructured formulations. In this paper, we present several important developments within this framework. These include the extension of a previous two phase flow finite volume formulation to the general black oil case, the implementation of techniques for treating systems in which grid lines do not match between adjacent subdomains, and the application of a near-well radial upscaling technique to the multiblock paradigm. Simulation results illustrating the accuracy and efficiency of these new capabilities are presented. These include a black oil simulation for a local well study, flow through a realistic reservoir with several wells and faults, flow through a fault surface represented by nonmatching grid lines, and a two phase flow simulation demonstrating the applicability of the near-well upscaling procedure to multiblock models. With the new developments presented in this paper, the finite volume based multiblock simulator can be applied to a variety of problems of practical interest. TX 75083-3836, U.S.A., fax 01-972-952-9435.