We analyze the impact of data from the full Run 1 of the LHC at 7 and 8 TeV on the CMSSM with μ > 0 and <0 and the NUHM1 with μ > 0, incorporating the constraints imposed by other experiments such as precision electroweak measurements, flavour measurements, the cosmological density of cold dark matter and the direct search for the scattering of dark matter particles in the LUX experiment. We use the following results from the LHC experiments: ATLAS searches for events with ET accompanied by jets with the full 7 and 8 TeV data, the ATLAS and CMS measurements of the mass of the Higgs boson, the CMS searches for heavy neutral Higgs bosons and a combination of the LHCb and CMS measurements of BR(Bs → μ+μ-) and BR(Bd → μ+μ-). Our results are based on samplings of the parameter spaces of the CMSSM for both μ >0 and μ <0 and of the NUHM1 for μ > 0 with 6.8 × 106, 6.2× 106 and 1.6× 107 points, respectively, obtained using the MultiNest tool. The impact of the Higgs-mass constraint is assessed using FeynHiggs 2.10.0, which provides an improved prediction for the masses of the MSSM Higgs bosons in the region of heavy squark masses. It yields in general larger values of Mh than previous versions of FeynHiggs, reducing the pressure on the CMSSM and NUHM1. We find that the global χ2 functions for the supersymmetric models vary slowly over most of the parameter spaces allowed by the Higgs-mass and the ET searches, with best-fit values that are comparable to the χ2/dof for the best Standard Model fit. We provide 95 % CL lower limits on the masses of various sparticles and assess the prospects for observing them during Run 2 of the LHC.