  This article gives a comprehensive review on the recent studies of the double
exchange systems using non-perturbative approaches; the dynamical mean-field
theory and the Monte Carlo method. Investigations beyond mean-field type
treatments are described. Taking into account strong spin fluctuations which
create large changes in conduction electron structure, finite temperature
properties as well as dynamics of the system are calculated. Comparisons with
experimental data for colossal magnetoresistance manganites are made. We show
that high Curie temperature (Tc) compounds, e.g. (La,Sr)MnO3, are canonical
double-exchange systems. Properties of other compounds with lower Tc are
discussed in relation to inhomogeneities of the system including the issue of
phase separation.
