  Theories of photoinduced phase transitions have developed along with the
progress in experimental studies, especially concerning their nonlinear
characters and transition dynamics. At an early stage, paths from photoinduced
local structural distortions to global ones are explained in classical
statistical models. Their dynamics are governed by transition probabilities and
inevitably stochastic, but they were sufficient to describe coarse-grained time
evolutions. Recently, however, a variety of dynamics including ultrafast ones
are observed in different electronic states. They are explained in relevant
electronic models. In particular, a coherent lattice oscillation and coherent
motion of a macroscopic domain boundary need appropriate interactions among
electrons and lattice displacements. Furthermore, some transitions proceed
almost in one direction, which can be explained by considering relevant
electronic processes. We describe the history of theories of photoinduced phase
transitions and discuss a future perspective.
