Simulation of large complex systems for the purpose of evaluating performance and exploring alternatives is a computationally slow process, currently still out of the domain of real-time applications. This paper overviews advances in three directions aimed at overcoming this limitation. First, based on developments in the theory of discrete event systems, concurrent simulation enables the extraction of information from a single simulation that would otherwise require multiple repeated simulations. This effectively provides simulation speedups of possibly orders of magnitude. A second direction attempts to use simulation for the purpose of obtaining a 'metamodel' of the actual system, i.e., an approximate 'surrogate' model which is computationally very fast, yet accurate. We specifically discuss the use of neural networks as metamodeling devices which may be trained through simulation. Finally, hierarchical simulation provides yet another means for speedup, a major challenge being the preservation of fidelity between hierarchical levels. In practice, using the statistical average of a high resolution level simulator output as the input for a lower resolution level causes significant loss of stochastic fidelity. We present an approach in which we cluster the high resolution simulation output into 'path bundles' as the input for the lower resolution level. The paper includes applications of these new directions to areas such as combat simulation and design of C3I systems.