This paper surveys some results in stochastic differential delay equations beginning with ”On stationary solutions of a stochastic differential equations” by K. Ito and M. Nisio, 1964, and also some results in stochastic stability beginning with the ”Stability of positive supermartingales” by R. Bucy, 1964. The problems discussed in this survey are the existence and uniqueness of solutions of s...

A general version of the Yamada-Watanabe and Engelbert results relating existence and uniqueness of strong and weak solutions for stochastic equations is given. The results apply to a wide variety of stochastic equations including classical stochastic differential equations, stochastic partial differential equations, and equations involving multiple time transformations.