Significant progress has been made to develop silicon pixel technologies for use in the vertex and tracker regions of the proposed Compact Linear Collider (CLIC) detector design. The electron-positron collisions generated by this linear accelerator provide a clean, low-radiation environment for the inner detectors. However, physics-driven performance targets, the CLIC beam structure, and occupancies from beam-induced backgrounds place challenging requirements on detector technologies for this region. A pixel pitch down to 25 x 25$mu$m$^{-2}$, material budget $leq$ 0.2-2$%X_0$ per layer, average power dissipation of down to 50mWcm$^{-2}$, position resolution of 3-7$mu$m, and timing resolution as low as 5ns are called for in the vertex and tracking detectors. To this aim, a comprehensive R&D programme is ongoing to design and test silicon pixel detectors to fulfil these specifications, including both monolithic and hybrid devices. These studies involve Allpix$^2$ Monte Carlo and TCAD simulations, advanced 65nm ASIC and sensor design, laboratory testing, and beam tests of individual modules to determine the required performance parameters. The characterisation and simulation modelling of these devices has also lead to the development of a set of tools and software within the CLIC detector and physics (CLICdp) collaboration. This publication will present recent results from the technologies being developed and tested in view of the CLIC vertex and tracking detector requirements, such as various monolithic CMOS sensors, and fine pitch hybrid assemblies with planar sensors.