Theory of Manganites
  In this review, the present status of theories for manganites is discussed. The complex phase diagrams of these materials, with a variety of spin-charge-orbital ordering tendencies, is addressed using mean-field and Monte Carlo simulation techniques. The stability of the charge-ordered states, such as the CE-state at half-doping, appears to originate, in part, in the topology of the zigzag chains present in those states. In addition, it is argued that phase separation tendencies are notorious in realistic models for Mn-oxides. They produce nanoscale clusters of competing phases, either through an electronic separation tendency or through the influence of disorder on first-order transitions. These inhomogeneities lead to a ``colossal'' magnetoresistance (CMR) effect, compatible with experiments. This brief review is based on a more extensive work recently presented [E. Dagotto, T. Hotta, and A. Moreo, Phys. Rep. {\bf 344}, 1 (2001)]. There, a comprehensive analysis of the experimental literature can be found. In real manganites, the tendencies toward inhomogeneous states are notorious in CMR regimes, in excellent agreement with the theoretical description outlined here. 
Takashi Hotta and Elbio Dagotto