Current-mediated downstream dispersal by the early developmental stages of fish in rivers is a common phenomenon. Knowledge of patterns and processes in the dispersal, or ‘drift’, of young fishes provides important information on spawning location and spawning success, habitat use, movement paths and flow-ecology relationships more generally, all of which are critical for effective river conservation and management. But despite the importance of such information, our understanding of the patterns and processes of the drift of the early life stages of riverine fishes is limited. Furthermore, riverine fish drift research has tended to occur in isolation from movement studies of other organisms, limiting its integration with higher level concepts and theory. This manuscript reviews the literature on the dispersal of young fishes in running waters. Relevant studies from all climatic zones and geographical regions are investigated, with particular attention given to the types and life history stages of fishes that drift and the seasonal and diel patterns of drifting. We then consider how fish enter the drift and their mode of drifting, attempting to reconcile a long-running discussion, under what we call the ‘active–passive conundrum’. We argue that, aside from eggs, the early stages of fish are not exclusively either passive or active drifters, but usually a mixture of the two, which we term ‘actipassive’ drift. Finally, we evaluate existing knowledge in the context of a general conceptual framework for movement ecology, identifying gaps in our understanding of the roles of internal state, navigation capacity, motion capacity, external factors and internal factors in influencing the dispersal process. © 2016, The Author(s).