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The advances in materials and biological sciences have necessitated the useof molecular simulations to study polymers. The Markov chain Monte Carlosimulations enable the sampling of relevant microstates of polymeric systems bytraversing paths that are impractical in molecular dynamics simulations.Several advances in applying Monte Carlo simulations to polymeric systems havebeen reported in recent decades. The proposed methods address samplingchallenges encountered in studying different aspects of polymeric systems.Tracking the above advances has become increasingly challenging due to theextensive literature generated in the field. Moreover, the incorporation of newmethods in the existing Monte Carlo simulation packages is cumbersome due totheir complexity. Identifying the foundational algorithms that are common todifferent methods can significantly ease their implementation and make themaccessible to the broader simulation community. The present chapter classifiesthe Monte Carlo methods for polymeric systems based on their objectives andstandard features of their algorithms. We begin the article by providing anoverview of advanced Monte Carlo techniques used for polymeric systems andtheir specific applications. We then classify the above techniques into twobroad categories: 1) Monte Carlo moves and 2) Advanced sampling schemes. Theformer category is further divided to distinguish the Monte Carlo moves in thecanonical and other ensembles. The advanced sampling schemes attempt to improveMonte Carlo sampling via approaches other than Monte Carlo moves. We use theabove classification to identify common features of the methods and derivegeneral expressions that explain their implementation. Such a strategy can helpreaders select the methods that are suitable for their study and developcomputer programs that can be easily modified to implement new methods.

Advanced Monte Carlo simulation techniques to study polymers under equilibrium conditions