The Compact Linear Collider (CLIC) is a high-energy high-luminosity linear electron-positron collider under development. It is foreseen to be built and operated in three stages, at centre-of-mass energies of 380 GeV, 1.5 TeV and 3 TeV, respectively. It offers a rich physics program including direct searches as well as the probing of new physics through a broad set of precision measurements of Standard Model processes, particularly in the Higgs-boson and top-quark sectors. The precision required for such measurements and the specific conditions imposed by the beam dimensions and time structure put strict requirements on the detector design and technology. This includes low-mass vertexing and tracking systems with small cells, highly granular imaging calorimeters, as well as a precise hit-time resolution and power-pulsed operation for all subsystems. A conceptual design for the CLIC detector system was published in 2012. Since then, ambitious R&D programmes for silicon vertex and tracking detectors, as well as for calorimeters have been pursued within the CLICdp, CALICE and FCAL collaborations, addressing the challenging detector requirements with innovative technologies. This report introduces the experimental environment and detector requirements at CLIC and reviews the current status and future plans for detector technology R&D.