  The purely leptonic rare decay Bs -> mu+mu- is very sensitive to
supersymmetric contributions which are free from the helicity suppression of
its Standard Model diagrams. The recent observation of the decay by the LHCb
experiment and the first determination of its branching fraction motivate a
review of their impact on the viable parameter space of supersymmetry. In this
paper we discuss the implications of the present and expected future accuracy
on BR(Bs -> mu+mu-) for constrained and unconstrained MSSM scenarios, in
relation to the results from direct SUSY searches and the Higgs data at the
LHC. While the constraints from BR(Bs -> mu+mu-) can be very important in
specific SUSY regions, we show that the current result, and even foreseen
future improvements in its accuracy, will leave a major fraction of the SUSY
parameter space, compatible with the results of direct searches, unconstrained.
We also highlight the complementarity of the Bs -> mu+mu- decay with direct
SUSY searches.
