  The ATLAS and CMS experiments have recently announced the discovery of a
Higgs-like resonance with mass close to 125 GeV. Overall, the data is
consistent with a Standard Model (SM)-like Higgs boson. Such a particle may
arise in the minimal supersymmetric extension of the SM with average stop
masses of the order of the TeV scale and a sizable stop mixing parameter. In
this article we discuss properties of the SM-like Higgs production and decay
rates induced by the possible presence of light staus and light stops. Light
staus can affect the decay rate of the Higgs into di-photons and, in the case
of sizable left-right mixing, induce an enhancement in this production channel
up to $\sim$ 50% of the Standard Model rate. Light stops may induce sizable
modifications of the Higgs gluon fusion production rate and correlated
modifications to the Higgs diphoton decay. Departures from SM values of the
bottom-quark and tau-lepton couplings to the Higgs can be obtained due to Higgs
mixing effects triggered by light third generation scalar superpartners. We
describe the phenomenological implications of light staus on searches for light
stops and non-standard Higgs bosons. Finally, we discuss the current status of
the search for light staus produced in association with sneutrinos, in final
states containing a $W$ gauge boson and a pair of $\tau$s.
