  Due to their intrinsic link with nonlinear Fokker-Planck equations and many
other applications, distribution dependent stochastic differential equations
(DDSDEs for short) have been intensively investigated. In this paper we
summarize some recent progresses in the study of DDSDEs, which include the
correspondence of weak solutions and nonlinear Fokker-Planck equations, the
well-posedness, regularity estimates, exponential ergodicity, long time large
deviations, and comparison theorems.
