An essential problem with the standard molecular dynamics (MD) and Monte Carlo (MC) techniques is their inefficiency to induce crossing of energy barriers, in particular, in protein and fluid systems. This chapter discusses several sophisticated techniques, based on MC and MD, which can overcome this problem at least partially; they are: “temperature and Hamiltonian replica exchange methods” and combinations of them, “the multicanonical method” the related “Wang and Landau technique” the “method of expanded ensembles” (called also simulated tempering), and “the adaptive integration procedure” (AIM). Like WHAM and Bennett’s methods, most of these techniques are based on a self-consistent procedure that also leads directly to free energy differences, ΔF; replica exchange, in this respect, is an outlier, which, however, can lead to ΔF if combined with WHAM, for example. Finally, “Jarzynski’s non-equilibrium method” is discussed. This method enables one calculating free energy differences, which, together with AIM, constitute an alternative to the free energy perturbation (FEP) and thermodynamic integrations (TI) methods discussed earlier in Chapter 17. All these methods have been tested extensively, and to gain further efficiency and to widen applicability hybrid methods have been created. Performance studies of some of these techniques, based on toy or simplified models, have been inconclusive. Therefore, the policy used here is to follow carefully applications of these methods in the literature, describing the systems studied in detail. The criterion of performance is based on the maximal system size and complexity that a method can handle. Replica exchange has been found in particular efficient.