Hybrid (discrete/continuous) systems exhibit both discrete state and continuous state dynamics which interact to such a significant extent that they cannot be decoupled and must be analyzed simultaneously. We present an overview of the work that has been done in the modeling, simulation, sensitivity analysis, and optimization of hybrid systems, paying particular attention to the interaction between discrete and continuous dynamics. A concise intuitive framework for hybrid system modeling is presented, together with discussions on robust state event location, transfer functions of the continuous state at discontinuities, parametric sensitivity analysis of hybrid systems, and challenges in optimization.