Asian monsoon rainfall impacts one third of the global population and predicting its variability and future change is of clear importance. However, the dynamics of even the climatological monsoon are not fully understood; seemingly unconnected behaviors and abrupt jumps in rainfall location occur in different regions through the year. Three independent subsystems have traditionally been considered: the East Asian, South Asian, and Western North Pacific monsoons. These are generally viewed as passive stationary-wave responses to insolation, but this picture cannot explain the abrupt jumps in rainfall location. Using model simulations, reanalysis and observations, we show that the complex behavior of all three subsystems in fact results from active propagation of the summertime ‘stationary’ wave. A continent-scale cyclone first expands northwestwards and then propagates eastwards via advective and evaporative feedbacks. We propose that the monsoon’s response to forcings may be understood by considering how this wave interacts with the background state.