This will be an introductory talk devoted to the study of random dynamics on the circle. I will discuss the (exponential) contraction (and Baxendale’s theorem), stationary measures, and generic alternative between minimality and existence of no-exit domains (in particular, following our work with Yu. Kudryashov and A. Okunev), and Yu. Ilyashenko and A. Negut’s «invisible parts of attractors».