  The current searches at the LHC have set strong bounds on the masses of
gluinos and the squarks of the first and second generation. At the same time,
the hints of a Higgs boson at 125 GeV imply some degree of fine-tuning from
radiative corrections to the lightest Higgs mass. Moreover, the rate into
photons seems to be enhanced with respect to the SM, while the ZZ channel is
reduced (albeit the SM is still compatible at the 2-sigma level). In this talk
I will review how the previous issues can be addressed. If the stop is about a
couple-hundred GeV, the SUSY still remains as a natural solution to the
hierarchy problem. I will also show how the MSSM can accommodate a 125 GeV
Higgs and also how extensions of the MSSM can alleviate the fine-tuning on the
Higgs mass. I will also discuss recent literature, showing how both in the MSSM
and its extensions one can find suitable ways to accommodate the measured Higgs
rates into photons and Z bosons.
