Many important social phenomena are characterized by repeated interactions among individuals over time such as email exchanges in an organization or face-to-face interactions in a classroom. To understand the underlying mechanisms of social interaction dynamics, statistical simulation techniques of longitudinal network data on a fine temporal granularity are crucially important. This paper makes two contributions to the field. First, we present statistical frameworks to simulate relational event networks under dyadic and actor-oriented relational event models which are implemented in a new R package 'remulate'. Second, we explain how the simulation framework can be used to address challenging problems in temporal social network analysis, such as model fit assessment, theory building, network intervention planning, making predictions, understanding the impact of network structures, to name a few. This is shown in three extensive case studies. In the first study, it is elaborated why simulation-based techniques are crucial for relational event model assessment which is illustrated for a network of criminal gangs. In the second study, it is shown how simulation techniques are important when building and extending theories about social phenomena which is illustrated via optimal distinctiveness theory. In the third study, we demonstrate how simulation techniques contribute to a better understanding of the longevity and the potential effect sizes of network interventions. Through these case studies and software, researchers will be able to better understand social interaction dynamics using relational event data from real-life networks.