  The advances in materials and biological sciences have necessitated the use
of molecular simulations to study polymers. The Markov chain Monte Carlo
simulations enable the sampling of relevant microstates of polymeric systems by
traversing paths that are impractical in molecular dynamics simulations.
Several advances in applying Monte Carlo simulations to polymeric systems have
been reported in recent decades. The proposed methods address sampling
challenges encountered in studying different aspects of polymeric systems.
Tracking the above advances has become increasingly challenging due to the
extensive literature generated in the field. Moreover, the incorporation of new
methods in the existing Monte Carlo simulation packages is cumbersome due to
their complexity. Identifying the foundational algorithms that are common to
different methods can significantly ease their implementation and make them
accessible to the broader simulation community. The present chapter classifies
the Monte Carlo methods for polymeric systems based on their objectives and
standard features of their algorithms. We begin the article by providing an
overview of advanced Monte Carlo techniques used for polymeric systems and
their specific applications. We then classify the above techniques into two
broad categories: 1) Monte Carlo moves and 2) Advanced sampling schemes. The
former category is further divided to distinguish the Monte Carlo moves in the
canonical and other ensembles. The advanced sampling schemes attempt to improve
Monte Carlo sampling via approaches other than Monte Carlo moves. We use the
above classification to identify common features of the methods and derive
general expressions that explain their implementation. Such a strategy can help
readers select the methods that are suitable for their study and develop
computer programs that can be easily modified to implement new methods.
