Physics not only describes past, present, and future events but also accounts for unrealized possibilities. These possibilities are represented through the solution spaces given by theories. These spaces are typically classified into two categories: kinematical and dynamical. The distinction raises important questions about the nature of physical possibility. How should we interpret the difference between kinematical and dynamical models? Do dynamical solutions represent genuine possibilities in the physical world? Should kinematical possibilities be viewed as mere logical or linguistic constructs, devoid (...) of a deeper connection to the structure of physical reality? This chapter addresses these questions by analyzing some of the most significant theories in physics: classical mechanics, general relativity and quantum mechanics, with a final mention to quantum gravity. We argue that only dynamical models correspond to genuine physical possibilities. (shrink)