This talk looks at the development of abstraction techniques based on quantitative approximations, in order to formally verify complex systems and to provide computable approaches for the correct-by-design synthesis of control architectures. The approach employs techniques and concepts from the formal verification area, such as that of bisimulation, over models and problems from the field of dynamical systems and control theory. While emphasising the generality of the approach over a diverse set of model classes, this talk zooms in on stochastic hybrid systems, which are probabilistic models with heterogeneous dynamics (continuous/discrete, i.e. hybrid, as well as nonlinear). A case study in energy networks, dealing with the problem of demand response, is employed to clarify concepts and techniques. Theory is complemented by algorithms, all packaged in software tools (called FAUST² for stochastic hybrid systems) that are freely available to users.