Telerehabilitation systems that support physical therapy sessions anywhere can help save healthcare costs while also improving the quality of life of the users that need rehabilitation. The main contribution of this paper is to present, as a whole, all the features supported by the innovative Kinect-based Telerehabilitation System (KiReS). In addition to the functionalities provided by current systems, it handles two new ones that could be incorporated into them, in order to give a step forward towards a new generation of telerehabilitation systems. The knowledge extraction functionality handles knowledge about the physical therapy record of patients and treatment protocols described in an ontology, named TRHONT, to select the adequate exercises for the rehabilitation of patients. The teleimmersion functionality provides a convenient, effective and user-friendly experience when performing the telerehabilitation, through a two-way real-time multimedia communication. The ontology contains about 2300 classes and 100 properties, and the system allows a reliable transmission of Kinect video depth, audio and skeleton data, being able to adapt to various network conditions. Moreover, the system has been tested with patients who suffered from shoulder disorders or total hip replacement.