  I briefly survey here attempts to model the rich and strange behaviour of
colossal magnetoresistance manganites, after outlining some of the phenomena
observed in them, and describing the three relevant strong local interactions
of the e_g electrons (in two different orbital states at each site), namely
with Jahn-Teller phonon modes (strength g), with resident t_2g spins
(ferromagnetic Hund's rule coupling J_H) and amongst each other (the Mott
Hubbard correlation U) . A new two fluid model of nearly localized l polarons
and band (b) electrons for low energy behaviour emerges for large g; some of
its applications are mentioned here. I describe some results of strong coupling
U, J_H calculations in single site DMFT (Dynamical Mean Field Theory), and show
that in the wide orbital liquid regime many characteristic manganite phenomena
such as an insulating ferromagnetic ground state, thermal insulator metal
transition, colossal magnetoresistance (cmr), materials systematics and the
observed low effective carrier density can all be understood qualitatively and
quantitatively. We also discuss the two 'phase' coexistence frequently found in
these systems, and show that electrostatic coulomb interactions mute lb phase
separation into nanoscale electronic inhomogeneity with l regions and b
puddles. Finally, some problems of current interest as well as general ones
arising, eg polarons and the physics of large electron phonon coupling g in the
adiabatic regime, are mentioned.
