In this thesis , w e analytically investigate the holographic superconductors with Lifshitz scaling in presence of nonlinear electrodynamics. The technique employed is based on the matching of the solutions to the field equations near the horizon and the asymptotic AdS region. First, we investigate the holographic superconductor model in the (d+1) dimensional Schwarzschild-AdS background with usual Maxwell electrodynamics and compute condensation and critical temperature of superconductor. Since the nonlinear electrodynamics to the usual Maxwell electrodynamics have the higher derivative corrections, much of the work presented in this thesis is concerned with nonlinear corrections. We investigate the effect of these corrections on holographic superconductivity and we will observe that the nonlinear corrections decrease critical temperature and make the condensation harder to occur. On the other hand, due to many condensed matter systems do not have relativistic symmetry, we are interested in generalizing the holographic superconducting models to nonrelativistic situations. Thus, we will work in the Lifshitz blackhole background that it results in nonrelativistic behaviors near the asymptotic AdS region. We find that the critical temperature decreases with the increase of the dynamical exponent z, which shows that Lifshitz scaling makes the condensation harder to occur. In latter part of this thesis, we employ the matching method to analytically investigate the effect of an external magnetic field on holographic superconductors with Lifshitz scaling in presence of nonlinear electrodynamics. We see that the well-known relation of the critical magnetic field from the Ginzburg-Landau theory can be reproduced in holographic superconductor with Lifshitz scaling in presence of nonlinear electrodynamics.