In this paper a brief overview of anomalous behavior resulting from the two-gap superconductivity in MgB2 is given. We focus on two characteristic effects: an anomalous enhancement of the upper critical field by nonmagnetic impurities and nonequilibrium interband phase textures which appear as a result of interband breakdown caused by electric field. Both effects distinguish MgB2 from the existing low-Tc and high-Tc superconductors.