The central philosophy of statistical mechanics and random-matrix theory of complex systems is that while individual instances are essentially intractable to simulate, the statistical properties of random ensembles obey simple universal “laws”. This same philosophy promises powerful methods for studying the dynamics of quantum information in ideal and noisy quantum circuits – for which classical description of individual circuits is expected to be generically intractable. In this tutorial-style talk, I will review recent progress in understanding the dynamics of quantum information in ensembles of random hybrid  (including measurements, dissipation etc.) quantum circuits through a stat. mech. lens. In particular, I will discuss how various quantities of interest can be computed using exact mappings onto replicated statistical mechanics models.