The physics aims at the proposed future high-energy linear e+e- collider CLIC pose challenging demands on the performance of the detector system. In particular, the vertex and tracking detectors have to combine a spatial resolution of a few micrometres and a low material budget with a time-stamping accuracy of a few nanoseconds. For the vertex detector, fine-pitch sensors, dedicated 65nm readout ASICs, fine-pitch bonding techniques using solder bumps or anisotropic conductive films as well as monolithic devices based on Silicon-On-Insulator technology are explored. Fully monolithic CMOS sensors with large and small collection electrodes are under investigation for the large surface CLIC tracker. This contribution gives an overview of the CLIC vertex and tracking detector R&D, focusing on recent results from test-beam campaigns and simulation-based sensor optimisation studies.