We make a critical study of two highly-constrained models of supersymmetry -the constrained minimal supersymmetric standard model (cMSSM), and the non-universal Higgs mass model (NUHM) -in the light of the 125-126 GeV Higgs boson, the first observation of Bs → µµ at the LHCb, and the updated B → τ ν branching ratio at BELLE. It turns out that these models are still allowed by the experimental data, even if we demand that there be a light stop with mass less than 1.5 TeV. The only significant effects of all these constraints are to push the mass of the light stop above ∼ 500 GeV, and to prefer the universal trilinear coupling A0 to be large and negative. We calculate the Higgs boson branching ratios to W W, ZZ, τ τ and γγ in these models and show that improved experimental limits on these could put them to the most stringent experimental tests yet. However, as this could be sheer coincidence, only the discovery of a superpartner of one of the known SM particles would really establish the existence of supersymmetry (SUSY). Now, the elevation of the light Higgs boson mass to a value above M Z ≈ 91 GeV in supersymmetric models is known [4] to be primarily due to radiative corrections involving the top quark (t) and the light and heavy stop states (t 1 ,t 2 ). It follows, therefore, that the discovery of a light Higgs boson candidate in the upper part of the SUSY-allowed range may be considered as a hint of the existence of a rather low-lying stop state (t 1 ) -perhaps light enough to be discovered at the LHC. We cannot, however, be too sure about this, for SUSY models can be practically indistinguishable from the SM if we take the so-called decoupling limit, where all the superpartners are too heavy to be detected at the LHC (or any terrestrial experiment conceivable in the near future).Faced with this situation, we approach the problem in a pragmatic way, viz. we focus on that part of the large SUSY parameter space that could support a light stop state discoverable at the LHC. Though this does resemble the proverbial search under the lamp post, at the present juncture, it seems the most reasonable thing to do. The question then arises as to how light thet 1 state must be. An exact answer is, of course, a matter of detail, but one can form a crude estimate based on the fact that the production oft 1t1 pairs at the LHC is dominated by strong interactions and hence depends essentially on the mass of thet 1 alone. The variation of thet 1t1 pair-production cross-section with mt 1 at the 14-TeV LHC is easily calculated [5], and this falls from a few pb at mt 1 ≃ 300 GeV to about 10 ab for mt 1 ≃ 1.5 TeV. As a typical estimate of the integrated luminosity of the LHC is about 3 ab −1 , the latter value corresponds to around 30t 1t1 pairswhich may be just enough for a discovery. Accordingly, we take mt 1 ≤ 1.5 TeV as a reasonable criterion for a possible LHC discovery of the light stop.This light stop criterion is not, however, the only restriction on the parameter space of the SUSY model in question. The requirement of a l...