The compelling astrophysical evidence for dark matter on one hand and the experimental evidence for neutrino masses on the other, demands modifications beyond the Standard Model. Therefore, building new models by extending the symmetries and particle content of the Standard Model is being pursued to remedy these problems. In this thesis, various models along with their predictions are presented. First, a gauge SU$(2)_N$ extension of the Standard Model, under which all of the Standard Model particles are singlet is introduced. The inverse seesaw mechanism is implemented for neutrino mass, with the new gauge boson as a dark matter candidate. The second paper is a gauge B-L extension of the Standard Model which breaks down to $\mathbb{Z}_3$, and it includes a long-lived dark matter candidate. The next model assumes that leptons do not couple directly to Higgs, and one loop mass generation is considered with important consequences, including Higgs decay, muon anomalous magnetic moment, etc. We then look at a U(1) gauge extension of the supersymmetric Standard Model, which has no $\mu$ term, and the Higgs boson's mass supersymmetric constraint is relaxed. The next model is a gauge B-L extension of the Standard Model with radiative seesaw neutrino mass and multipartite dark matter. We then consider another gauge U(1) extension under which quarks and leptons of each family may transform differently, while flavor-changing interactions are suitably suppressed. The next paper has an unbroken gauge SU(2) symmetry, which becomes confining at keV scale. We discuss the cosmological constraints and the implications for future $e^+e^-$ colliders. Finally, an alternative left-right model is proposed with an automatic residual $Z_2\times Z_3$ symmetry, such that dark matter has two components, i.e., one Dirac fermion and one complex scalar.