Event cameras are novel sensors that report brightness changes in the form of a stream of asynchronous events instead of intensity frames. They offer significant advantages with respect to conventional cameras: high temporal resolution, high dynamic range, and no motion blur. In this work we propose to learn to reconstruct intensity images from event streams directly from data instead of relying on any hand-crafted priors. We propose a novel recurrent network to reconstruct videos from a stream of events, and train it on a large amount of simulated event data. We show that the network is able to synthesize high framerate videos (> 5,000 frames per second) of high-speed phenomena (e.g. a bullet hitting an object) and is able to provide high dynamic range reconstructions in challenging lighting conditions.