With the development of investigations in mesoscopic systems such as the cellular systems, growing attention has been focused on the corresponding reaction dynamics simulation methods. For one thing, fluctuations are significant in these systems, chemical reactions are essentially discrete stochastic processes, classical deterministic algorithms are not feasible, stochastic simulation methods are required. For another, there are multiscale characters in these systems. The coexistence of fast and slow sub-reactions produce multi-time scales and the different molecular abundance of various reactants exhibit multi-population scales, These multiscale characters will considerably reduce the simulation efficiency of stochastic algorithms. Therefore, there are even higher requirements for accurate but efficient reaction dynamics simulation algorithms. In this paper, we first summarize the basic stochastic simulation algorithms developed by Gillespie, then review the recently proposed improved stochastic algorithms and hybrid methods which are developed to circumvent the multiscaled problems. The special characters, the technical problems involved in the implementation and the advantages and disadvantages of these algorithms are introduced. Contents
1 Stochastic algorithms for chemical reaction
2 Improved stochastic algorithms for stiff systems
2.1 Implicit numerical methods
2.2 Approximate algorithms based on quasi-steady-state assumption and partial equilibrium assumption
3 Hybrid algorithms
3.1 Partition criterion
3.2 Synchronous transformation