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An overview of advanced dynamical algorithms capable of spanning the widelydisparate time scales that govern the decay of metastable phases in discretespin models is presented. The algorithms discussed include constrainedtransfer-matrix, Monte Carlo with Absorbing Markov Chains (MCAMC), andprojective dynamics (PD) methods. The strengths and weaknesses of each of thesealgorithms are discussed, with particular emphasis on identifying the parameterregimes (system size, temperature, and field) in which each algorithm worksbest.Comment: 12 pages, 4 figures, proceedings of the US-Japan bilateral seminar on  `Understanding and Conquering Long Time Scales in Computer Simulations', July  1999, to appear in Int. J. Mod. Phys.

ADVANCED DYNAMIC ALGORITHMS FOR THE DECAY OF METASTABLE PHASES IN DISCRETE SPIN MODELS: BRIDGING DISPARATE TIME SCALES