We analyze the extent to which the LHC and Tevatron results as of the end of 2012 constrain invisible (or undetected) decays of the Higgs boson-like state at ~ 125 GeV. To this end we perform global fits for several cases: 1) a Higgs boson with Standard Model (SM) couplings but additional invisible decay modes; 2) SM couplings to fermions and vector bosons, but allowing for additional new particles modifying the effective Higgs couplings to gluons and photons; 3) no new particles in the loops but tree-level Higgs couplings to the up-quarks, down-quarks and vector bosons, relative to the SM, treated as free parameters. We find that in the three cases invisible decay rates of 23%, 61%, 88%, respectively, are consistent with current data at 95% confidence level (CL). Limiting the coupling to vector bosons, CV, to CV < 1 in case 3) reduces the allowed invisible branching ratio to 56% at 95% CL. Requiring in addition that the Higgs couplings to quarks have the same sign as in the SM, an invisible rate of up to 36% is allowed at 95% CL. We also discuss direct probes of invisible Higgs decays, as well as the interplay with dark matter searches.