In this thesis, we investigate some properties of high temperature holographic superconductors. Using the matching method, some properties of holographic superconductors are described analytically for a simple model. For this model, in the Lifshitz black hole background and by neglecting the effects of back reaction, we investigate the behavior of critical temperature, expectation value of condensation operator and critical magnetic field. For example, increasing Lifshitz dynamical exponent, z , indicating that condensation becomes difficult. In addition, using the same method, we study the Weyl superconductors. Assuming a coupling between the gauge field and the curvature of space time and study the effect of this coupling on critical temperature, expectation value of condensation operator and the critical magnetic field . In these models, we consider the probe limit where the effects of back reaction is negligible. For a nonlinear electrodynamic model, assuming the back reaction effect is not negligible and using Sturm-Liouville method, we calculate the condensation, critical temperature and the critical magnetic field in the Lifshitz black hole back ground. Our result indicate that back reaction effect has an important role in the value of condensation operator, critical temperature and critical magnetic field. In another part of thesis, we investigate the superconductor phase transition using the holographic entanglement entropy and also other topological invariants of the RT surface and the volume enclosed by it. These topological invariants provide a clearer illustration of the superconductor phase transition than do the holographic entangelment entropy. In addition, in the Lifshitz black hole background and for a nonlinear electrodynamic, we study the behaviour of conductivity in our model.