We begin with a pedagogical introduction to the Physics of the Mott Insulator to Superfluid transition (MI-SF)and its recent realization in cold-atomic system. Then we elaborate on such MI-SF transition in systems with two species of ultra-cold bosonic atoms in a two-dimensional square optical lattice with nearest- neighbor hopping amplitude t and a spin-orbit coupling k_SO. We chart out the phase diagram for the MI-SF transition using both a strong-coupling expansion and Gutzwiller mean-field theory. The momentum distribution near the MI-SF transition is shown to give precursor peaks. We analyze the critical theory of the transition revealing the presence of unconventional quantum critical points at t/k_SO=0, which are accompanied by the emergence of an additional gapless mode in the critical region. The Gutzwiller mean-field theory shows the existence of a twisted superfluid phase. We study the distribution of phases and the magnitude of the SF order parameter as a function of t and k_SO. We also study the collective modes and the dynamics of the phases in the semi-classical approach.