Abstarct: For a long time, it was believed that neutrinos were massless, spin-half particles, making them drastically different from their other standard model spin-half cousins such as the charged leptons (e, μ, τ) and the quarks (u, d, s, c, t, b), which are known to have mass. In fact, the masslessness of the neutrino was considered so sacred in the 1950s and 1960s that the fundamental law of weak interaction physics, the successful V-A theory for charged current weak processes proposed by Sudarshan, Marshak, Feynman and Gell-Mann, was considered to be intimately lixnked to this fact. The argument went as follows: a massless fermion field equation is invariant under the γ5 transformation; since the neutrino is one such particle and it participates exclusively in weak interactions. The accumulating evidences for neutrino mass from the solar and atmospheric neutrino data compiled in the 1990s and still are ongoing. However the possibility of a nonzero neutrino mass at phenomenological level goes back almost 1970s. In the context of gauge theories, they were discussed extensively in the1970s and 1980s long before there was any firm evidence for it. The existence of a nonzero neutrino mass makes neutrinos more like the quarks, and allows for mixing between the different neutrino flavors leading to the phenomenon of neutrino oscillation. More importantly, the simple fact that neutrino masses vanish in the standard model implies that evidence for neutrino mass is solid evidence for the existence of new physics beyond the standard model. The standard model itself is baxsed on the gauge group and neutrinos are massless particles within it. Existence of many observed evidences for neutrino masses besides other problems of standard model implies that one must seek physics beyond the standard model to explain them. This does not necessarily mean going beyond the gauge group of the standard model. Standard model is very successful in describing many phenomena. Even with the same gauge group as the standard model, one can makes models so that the model predicts massive neutrinos. In this thesis, I will discuss some such simple modifications of the standard model to describe the massive neutrinos.