The ATLAS experiment at the LHC has measured the Higgs boson couplings and mass, and searched for invisible Higgs boson decays, using multiple production and decay channels with up to 4.7 fb−1 of pp collision data at √s=7 TeV and 20.3 fb−1 at √s=8 TeV. In the current study, the measured production and decay rates of the observed Higgs boson in the γγ, ZZ, W W , Zγ, bb, τ τ , and μμ decay channels, along with results from the associated production of a Higgs boson with a top-quark pair, are used to probe the scaling of the couplings with mass. Limits are set on parameters in extensions of the Standard Model including a composite Higgs boson, an additional electroweak singlet, and two-Higgs-doublet models. Together with the measured mass of the scalar Higgs boson in the γγ and ZZ decay modes, a lower limit is set on the pseudoscalar Higgs boson mass of m A > 370 GeV in the “hMSSM” simplified Minimal Supersymmetric Standard Model. Results from direct searches for heavy Higgs bosons are also interpreted in the hMSSM. Direct searches for invisible Higgs boson decays in the vector-boson fusion and associated production of a Higgs boson with W/Z (Z → ℓℓ, W/Z → jj) modes are statistically combined to set an upper limit on the Higgs boson invisible branching ratio of 0.25. The use of the measured visible decay rates in a more general coupling fit improves the upper limit to 0.23, constraining a Higgs portal model of dark matter.