A general method, namely coherent-anomaly method (CAM) for phase transitions and critical phenomena using generalized cluster-mean-field approximations is explained briefly together with the overview of its applications to spin systems and other several many-body systems. The conceptual meaning of the CAM is emphasized here as well as its technical usefulness is stressed. A new drastic method for studying itinerant electron systems is proposed with some possible applications to the Hubbard model, quantum spin systems and high-T_c superconductors.