  Based on the model combining the spin double exchange and the lattice
polaron, we have studied the colossal magnetoresistance phenomena observed in
perovskite manganites R_{1-x}A_xMnO_3. First, effects of both the double
exchange and the electron-phonon interaction on the transport property are
investigated. We have evaluated the temperature dependent resistance and the
magnetoresistance using the Kubo formula, and examined the crossover from
tunneling to hopping regime of small polarons. Second, effects of the double
exchange interaction on the lattice degree of freedom are explored. It is found
that both the hardening of the phonon frequency and the reduction of the phonon
damping take place with decreasing the temperature.
