The Compact Linear Collider (CLIC) is a mature option for a future electron-positron collider operating at centre-of-mass energies of up to 3 TeV. CLIC will be built and operated in a staged approach with three centre-of-mass energy stages currently assumed to be 380 GeV, 1.5 TeV and 3 TeV. This contribution discusses the physics potential of CLIC in the area of Higgs physics based on benchmark analyses using full detector simulations . The initial stage of operation allows study of Higgs production in Higgsstrahlung and WW-fusion, resulting in precise measurements of the production cross sections and the total Higgs-boson decay width. Operation at high energy will provide high-statistics samples of Higgs bosons produced in WW-fusion enabling tight constraints on Higgs couplings. High-energy operation also gives access to the ttH process and Higgs self-coupling, through the measurement of double Higgs production. Global fits to all possible measurements at CLIC are presented.
 Eur. Phys. J. C77, 475 (2017)