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The basic problem in equilibrium statistical mechanics is to compute phase space average, in which Monte Carlo method plays a very important role. We begin with a review of nonlocal algorithms for Markov chain Monte Carlo simulation in statistical physics. We discuss their advantages, applications, and some challenge problems which are still awaiting for better solutions. We discuss some of the recent development in simulation where reweighting is used, such as histogram methods and multicanonical method. We then discuss the transition matrix Monte Carlo method and associated algorithms. The transition matrix method offers an efficient way to compute the density of states. Thus entropy and free energy, as well as the usual thermodynamic averages, are obtained as functions of model parameter (e.g. temperature) in a single run. New sampling algorithms, such as the flat histogram algorithm and equal-hit algorithm, offer sampling techniques which generate uniform probability distribution for some chosen macroscopic variable.

Monte Carlo is a versatile and frequently used tool in statistical physics and beyond. Correspondingly, the number of algorithms and variants reported in the literature is vast, and an overview is not easy to achieve. In this pedagogical review, we start by presenting the probabilistic concepts which are at the basis of the Monte Carlo method. From these concepts the relevant free parameters--which still may be adjusted--are identified. Having identified these parameters, most of the tangled mass of methods and algorithms in statistical physics Monte Carlo can be regarded as realizations of merely a handful of basic strategies which are employed in order to improve convergence of a Monte Carlo computation. Once the notations introduced are available, many of the most widely used Monte Carlo methods and algorithms can be formulated in a few lines. In such a formulation, the core ideas are exposed and possible generalizations of the methods are less obscured by the details of a particular algorithm.