The Compact Linear Collider is a candidate to be the next high-energy particle physics collider. Using a novel acceleration technique, electrons and positrons would be brought into collision with a centre-of-mass energy of up to 3 TeV. Despite challenging levels of beam-induced background, this would provide a relatively clean environment in which to perform precision physics measurements. The vertex detector would be crucial in achieving this, and would need to provide accurate particle tracking information to facilitate secondary vertex reconstruction and jet flavour-tagging. With this goal in mind, current technological limits are being stretched to design a low occupancy, low mass and low-power dissipation vertex detector for CLIC. A concept comprising thin hybrid pixel detectors coupled to high-performance readout ASICs, power-pulsing and air-flow cooling is under development. In this paper, the CLIC vertex detector requirements are reviewed and the current status of R&D on sensors, readout, powering, cooling and supports is presented.