The dissertation is focused on algorithms for performing non-spatial and spatial stochastic simulations of reaction networks and on the exploration of improved or alternative approaches. Central topics are the evaluation and a subsequent comparison of algorithm performance in terms of execution speed and accuracy, the extension of temporal leap methods to the spatial realm as well as the introduction of a variant for a parallel execution, and the realization of a multi-algorithm simulation which introduces inter-rules to forge a link between the synchronized execution of subsidiary algorithms.