Random periodicity is ubiquitous in the real world. In this talk, I will provide the concepts of random periodic paths and periodic measures to mathematically describe random periodicity. It is proved that these two different notions are “equivalent”. Existence and uniqueness of random periodic paths and periodic measures for certain stochastic differential equations are proved. An ergodic theory is established. It is proved that for a Markovian random dynamical system, in the random periodic case, the infinitesimal generator of its Markovian semigroup has infinite number of equally placed simple eigenvalues including $0$ on the imaginary axis. This is in contrast to the mixing stationary case in which the Koopman-von Neumann Theorem says there is only one eigenvalue $0$, which is simple, on the imaginary axis. Geometric ergodicity for some stochastic systems is obtained. Possible applications e.g. in stochastic resonance will be discussed.