One of the great quests of science and engineering is to understand, model, replicate and eventually predict and design complex stochastic systems and their dynamics. For instance, model and parameter inference from data is a highly non-trivial task and tools such as sensitivity analysis and structural identifiability are required. In this talk, we present recent advances in sensitivity analysis for stochastic dynamics and discuss uncertainty quantification tools for bounding weak errors between probability distributions. New results on sensitivity analysis and uncertainty quantification for rare events are also presented. Finally, we setup an inference problem from pathway signaling, raise interesting questions and provide a first attempt for solving it.