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We present a review of recent work on circuit simulation techniques which are "third generation" in that they go beyond the Sparse Gauss Elimination, Newton Iteration, Stiff Implicit time integration approach which mark second-generation circuit simulators such as SPICE-II and ASTAP-II. Third generation simulators such as MOTIS, DIANA, and SPLICE have rejected one or more of these principal features in their quest for size and speed capabilities commensurate with the requirements of the VLSI era. We attempt to present a unified treatment of the various and disparate types of third generation simulators based on the concepts of large-scale decomposition theory. In particular we shall describe and classify simulators in terms of the role played by certain matrix forms in their formulation, namely Bordered Block Diagonal (BBD), Bordered Block Triangular (BBT), and Bordered Lower Triangular (BLT).