Searches for invisible decays of the Higgs boson are presented. The data collected with the CMS detector at the LHC correspond to integrated luminosities of 5.1, 19.7, and 2.3 inverse femtobarns at centre-of-mass energies of 7, 8, and 13 TeV, respectively. The search channels target Higgs boson production via gluon fusion, vector boson fusion, and in association with a vector boson. Upper limits are placed on the branching fraction of the Higgs boson decay to invisible particles, as a function of the assumed production cross sections. The combination of all channels, assuming standard model production, yields an observed (expected) upper limit on the invisible branching fraction of 0.24 (0.23) at the 95% confidence level. The results are also interpreted in the context of Higgs-portal dark matter models.