The Standard Model of particle physics is a very well tested theory today. There are some theoretical as well as experimental deficiencies in the Standard Model which hint for theories beyond the Standard Model. Any such theory may be tested by direct observation of some new particles, predicted by the theory, at High Energy Colliders, like the Large Hadron Collider(LHC). Since there has been no such particle detected till today, we need to study these new theories under the phenomenological aspects of our known experimental results. Such studies result in constraining the free parameter space of these models. In this thesis, we use experimental results from three different experiments at the LHC, namely the ATLAS experiment, the CMS experiment and the LHC-b experiment to constrain the parameter spaces of some of these models. The models discussed in this thesis are basically constructed by making minimal extensions in scalar and gauge structures of the Standard Model. We apply constraints on these models from the flavor physics observables which are mainly coming from the rare decays of B-mesons and are measured by the particle physics experiment, LHC-beauty (LHCb). In our study we also discuss some supersymmetric extensions of the Standard Model in light of the latest results on masses of particles and their superpartners (sparticles) provided by the ATLAS and the CMS experiments. It is also seen that the supersymmetric extensions of the Standard Model can provide a suitable dark matter candidate, the neutralino, with several coannihilation scenarios while having compatibilitywithallrecentexperimentalconstraintsfrom B-physicsandthesparticles mass bounds. Direct and indirect dark matter searches by XENON1t and Fermi-LAT collaborations are also incorporated to the studies of these models by measuring the dark matter relic density as well as spin-dependent and spin-independent cross sections forsomesampledatapoints. Compatibility ofsolutionswith Yukawa unifiedtheoriesis alsosearchedforthegaugesymmetrybasedsupersymmetricextensionsoftheStandard Model. We have also searched how the anomaly associated with the magnetic moment of muon can be solved within the context of the supersymmetric extensions of the Standard Model, in addition to all other constraints.