  This is the written version of a talk given by S.K. at the $10^{th}$
International Conference on High Energy and Astroparticle, Constantine,
Algeria. We briefly review the Standard Model (SM) and the major evidences and
main direction of physics beyond the SM (BSM). We introduce supersymmetry, as
one of the well-motivated BSM. Basic introduction to Minimal Supersymmetric
Standard Model (MSSM) is given. We analyze the thermal relic abundance of
lightest neutralino, which is the Lightest Supersymmetric Particle (LSP) in the
MSSM. We show that the combined Large Hadron Collider (LHC) and relic abundance
constraints rule out most of the MSSM parameter space except a very narrow
region. We also review non-minimal SUSY model, based on the gauge group
$SU(3)_C \times SU(2)_L \times U(1)_Y \times U(1)_{B-L}$ (BLSSM), where an
Inverse Seesaw mechanism of light neutrino mass generation is naturally
implemented. The phenomenological implications of this type of model at the
Large Hadron Collider (LHC) are analyzed.
