Direct methods for visual odometry (VO) have gained popularity for their capability to exploit information from all intensity gradients in the image. However, low computational speed as well as missing guarantees for optimality and consistency are limiting factors of direct methods, in which established feature-based methods succeed instead. Based on these considerations, we propose a semidirect VO (SVO) that uses direct methods to track and triangulate pixels that are characterized by high image gradients, but relies on proven feature-based methods for joint optimization of structure and motion. Together with a robust probabilistic depth estimation algorithm, this enables us to efficiently track pixels lying on weak corners and edges in environments with little or high-frequency texture. We further demonstrate that the algorithm can easily be extended to multiple cameras, to track edges, to include motion priors, and to enable the use of very large field of view cameras, such as fisheye and catadioptric ones. Experimental evaluation on benchmark datasets shows that the algorithm is significantly faster than the state of the art while achieving highly competitive accuracy.