critical summary of the recent developments in high temperature superconductivity is given. Physical properties of the new materials are summarized. The new theories proposed to explain high Tc are reviewed. In the case of a special type anisotropic gap, the currents and conductivity for single particle tunneling in high Tc superconductor junctions are calculated. Tunneling is assumed to be specular. The position of the peak in the conductivity curve, is found to be determined by the shape of the Fermi surface. Two geometries are considered: tunneling paxallel and perpendicular to CuO^ planes. The order of the peaks for these two configurations turns out to be opposite to experimental results. It is concluded that, conventional one band theory of superconductivity is not enough to explain observed tunneling spectra of high Tc superconductors.