  Stochastic hybrid systems have received significant attentions as a relevant
modelling framework describing many systems, from engineering to the life
sciences: they enable the study of numerous applications, including
transportation networks, biological systems and chemical reaction networks,
smart energy and power grids, and beyond. Automated verification and policy
synthesis for stochastic hybrid systems can be inherently challenging: this is
due to the heterogeneity of their dynamics (presence of continuous and discrete
components), the presence of uncertainty, and in some applications the large
dimension of state and input sets. Over the past few years, a few hundred
articles have investigated these models, and developed diverse and powerful
approaches to mitigate difficulties encountered in the analysis and synthesis
of such complex stochastic systems. In this survey, we overview the most recent
results in the literature and discuss different approaches, including
(in)finite abstractions, verification and synthesis for temporal logic
specifications, stochastic similarity relations, (control) barrier
certificates, compositional techniques, and a selection of results on
continuous-time stochastic systems; we finally survey recently developed
software tools that implement the discussed approaches. Throughout the
manuscript we discuss a few open topics to be considered as potential future
research directions: we hope that this survey will guide younger researchers
through a comprehensive understanding of the various challenges, tools, and
solutions in this enticing and rich scientific area.
