The apparent discovery of a Higgs boson with mass ∼125 GeV has had a significant impact on the constrained minimal supersymmetric extension of the Standard Model (the CMSSM). Much of the low-mass parameter space in the CMSSM has been excluded by supersymmetric particle searches at the LHC as well as by the Higgs mass measurement and the emergent signal for Bs → μ+ μ-. Here, we consider the impact of these recent LHC results on several variants of the CMSSM with a primary focus on obtaining a Higgs mass of ∼125 GeV. In particular, we consider the one- and two-parameter extensions of the CMSSM with one or both of the Higgs masses set independently of the common sfermion mass, m0 (the NUHM1,2). We also consider the one-parameter extension of the CMSSM in which the input universality scale Min is below the GUT scale (the sub-GUT CMSSM). Finally, we reconsider mSUGRA models with sub-GUT universality, which have the same number of parameters as the CMSSM. We find that when Min < MGUT large regions of parameter space open up where the relic density of neutralinos can successfully account for dark matter with a Higgs boson mass ∼125 GeV. Interestingly, we find that the preferred range of the A-term in sub-GUT mSUGRA models straddles that predicted by the simplest Polonyi model.