  The `$\mu$ from $\nu$' supersymmetric standard model ($\mu\nu$SSM) solves the
$\mu$ problem of supersymmetric models and reproduces neutrino data, simply
using couplings with the three families of right-handed neutrinos $\nu$'s.
Novel signatures of supersymmetry at the LHC are expected through these new
states, and couplings breaking $R$ parity. All supersymmetric particles are
potential candidates for the lightest one, which is not stable leading to
prompt or displaced vertices and producing final states with
multi-leptons/taus/jets/photons and missing energy. Besides, a decaying
gravitino turns out to be an interesting candidate for dark matter. It can be
searched through gamma-ray observations, such as those of the Fermi Large Area
Telescope. The latter, depending on the region of the parameter space of the
model, already imposes an upper bound on the gravitino mass of the order of
$5-20$ GeV and a lower bound on the lifetime of about $10^{25-28}$ s.
