We consider recent progress in algorithms for generating gauge field configurations that include the dynamical effects of light fermions. We survey what has been achieved in recent state-of-the-art computations, and examine the trade-offs between performance and control of systematic errors. We briefly review the use of polynomial and rational approximations in Hybrid Monte Carlo algorithms, and some of the theory of on-shell chiral fermions on the lattice. This provides a theoretical framework within which we compare algorithmic alternatives for their implementation; and again we examine the trade-offs between speed and error control.
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