The idea regarding stochastic differential equations as stochastic dynamical systems went back to late1970's. Later this was developed to include infinite dimensional cases such as stochastic functional differential equations and stochastic partial differential equations. With these foundational works in hands, to study the long time behaviour lies in the centre of the theory of stochastic dynamical systems. Fixed points and periodic paths are two basic notions in the theory of dynamical systems capturing their long time behaviour and equilibrium. The concept of the stationary solution has been known for some time and is the corresponding notion of fixed points in the stochastic counterpart. Moreover, it is well known that a stationary solution gives rise to the existence of an invariant measure. The notion of random periodic solutions is the stochastic counterpart of the periodic solution in the theory of dynamical systems. It describes random periodicity in many real world phenomena. In this talk, I will talk about the motivation to develop this work from points of view of both mathematics and applications. I will also talk about tools. They include the pull-back method and the infinite horizon forward and backward stochastic integral equations method. The latter method is applicable to non-dissipative SDEs and SPDEs. In this case, r.p.s. depends on the whole history of noise and therefore is not adapted but anticipating. I will also discuss the connection of random periodic solutions, periodic measures and invariant measures.