This paper advances a novel markerless hand tracking method for interactive applications. FullHand uses input from RGB and depth cameras in a desktop setting. It combines, in a voting scheme, a discriminative, part-based pose retrieval with a generative pose estimation method based on local optimization. We develop this approach to enable: (1) capturing hand articulations with high number of degrees of freedom, including the motion of all fingers, (2) sufficient precision, shown in a dataset of user-generated gestures, and (3) a high framerate of 50 fps for one hand. We discuss the design of free-hand interactions with the tracker and present several demonstrations ranging from simple (few DOFs) to complex (finger individuation plus global hand motion), including mouse operation, a first-person shooter and virtual globe navigation. A user study on the latter shows that free-hand interactions implemented for the tracker can equal mouse-based interactions in user performance.