We present EVO, an Event-based Visual Odometry algorithm. Our algorithm successfully leverages the outstanding properties of event cameras to track fast camera motions while recovering a semi-dense 3D map of the environment. The implementation runs in real-time on a standard CPU and outputs up to several hundred pose estimates per second. Due to the nature of event cameras, our algorithm is unaffected by motion blur and operates very well in challenging, high dynamic range conditions with strong illumination changes. To achieve this, we combine a novel, event-based tracking approach based on image-to-model alignment with a recent event-based 3D reconstruction algorithm in a parallel fashion. Additionally, we show that the output of our pipeline can be used to reconstruct intensity images from the binary event stream, though our algorithm does not require such intensity information. We believe that this work makes significant progress in SLAM by unlocking the potential of event cameras. This allows us to tackle challenging scenarios that are currently inaccessible to standard cameras.