In this paper we present the concept of cognitive satellite terrestrial radios (CSTR) for hybrid satellite-terrestrial systems (HSTS). The cognitive radio (CR) technology is being motivated by the radio regulatory bodies for efficient utilization of the radio spectrum. The future satellite ground terminals therefore need to integrate and co-exist with the spectrally crowded terrestrial wireless systems and hence we propose the idea of CSTR. The key issues are addressed and the concepts of developing CR based satellite ground terminals in HSTS for dynamic spectrum access on the ground are presented. Furthermore, the concept of 3D-Spatial reuse of the spectrum is also presented using the CSTR considering low elevated satellite ground stations. Two particular HSTS applications to illustrate the CSTR concept, a) the hybrid satellite-UWB (ultra wideband) communication system for personal area networks (PAN) with short range on ground communications, and b) the hybrid satellite-WRAN (wireless regional area networks) for long range on ground communications are presented. In both the applications the satellite uplink and the terrestrial radios adopt the CR functionalities. The key enabling technologies and their integrated architecture for the CSTR are also presented.