The evolution of flapping flight in bats from an arboreal gliding ancestor appears on the surface to be a relatively simple transition. However, bat flight is a highly complex functional system from a morphological, physiological, and aerodynamic perspective, and the transition from a gliding precursor may involve functional discontinuities that represent evolutionary hurdles. In this review, I suggest a framework for a comprehensive treatment of the evolution of complex functional systems that emphasizes a mechanistic understanding of the initial state, the final state, and the proposed transitional states. In this case, bats represent the final state and extant mammalian gliders are used as a model for the initial state. To explore possible transitional states, I propose a set of criteria for evaluating hypotheses about the evolution of flight in vertebrates and suggest methods by which we can advance our understanding of the transition from gliding to flapping flight. Although it is impossible ever to know with certainty the sequence of events landing to flapping flight, the field of possibilities can be narrowed to those that maintain the functional continuity of the wing and result in improved aerodynamic performance across this transition. The fundamental differences between gliding and flapping flight should not necessarily be seen as evidence that this transition could not occur; rather, these differences point out compelling aspects of the aerodynamics of animal wings that require further investigation.