We perform a parameter scan of the phenomenological Minimal Supersymmetric Standard Model (pMSSM) with eight parameters taking into account the experimental Higgs boson results from Run I of the LHC and further low-energy observables. We investigate various MSSM interpretations of the Higgs signal at 125 GeV. First, we consider the case where the light CP-even Higgs boson of the MSSM is identified with the discovered Higgs boson. In this case it can impersonate the SM Higgs-like signal either in the decoupling limit, or in the limit of alignment without decoupling. In the latter case, the other states in the Higgs sector can also be light, offering good prospects for upcoming LHC searches and for searches at future colliders. Second, we demonstrate that the heavy CP-even Higgs boson is still a viable candidate to explain the Higgs signal - albeit only in a highly constrained parameter region, that will be probed by LHC searches for the CP-odd Higgs boson and the charged Higgs boson in the near future. As a guidance for such searches we provide new benchmark scenarios that can be employed to maximize the sensitivity of the experimental analysis to this interpretation.