<p>This paper addresses modeling, controllability, and control analysis in three extensions of Petri nets (PNs) that integrate continuous and discrete dynamics: Timed Continuous Petri Nets (TCPNs), First-Order Hybrid Petri Nets (FOHPNs), and Generalized Batches Petri Nets (GBPNs). These formalisms extend the PN paradigm to capture hybrid behaviors in complex dynamical systems while preserving their structural and analytical foundations. Regarding TCPNs, results on controllability from a structural perspective are recalled, and the design of controllers based on a Model Predictive Control (MPC) approach is presented. The FOHPN model is described in detail, and a series of applications to real systems is discussed. Two different control approaches are considered: a myopic approach, which computes the instantaneous firing speeds of transitions as the solution of an optimization problem that varies at each macro-period, and an MPC-based approach, which overcomes some of the limitations of the myopic approach. For GBPNs, a semantics inspired by FOHPNs is revisited, combining discrete, continuous, and batch dynamics. This formalism enables control over firing flows and batch transfer speeds, leading to controllable GBPNs. Within this framework, and in the absence of discrete nodes or over a macro-period, three event-driven ON/OFF control strategies are examined. Together, these results highlight the potential of Continuous and Hybrid PN extensions to provide a unified foundation for the analysis and control of hybrid dynamical systems, bridging discrete-event and continuous-flow representations.</p>