Analysis and design methods for stochastic hybrid dynamical systems are presented. Analysis methods include reachability analysis as well as statistical approaches. System refinement and decomposition are explored as possible approaches to deal with complexity. Findings show that analysis of this class of systems is not scalable. A promising approach is demonstrated which relies on the automatic construction of decentralized control systems using desirable properties as constraints. The synthesized system does not require to be analyzed thereby cutting the analysis effort. This approach is promising but for now limited in its use.