Rough stochastic differential equations (RSDEs) are common generalisations of Itô SDEs and Lyons RDEs and have emerged as a new tool in several areas of applied probability, including non-linear stochastic filtering, pathwise stochastic optimal control, volatility modelling in finance and mean-fields analysis of the common noise system. We here take a unified perspective on rough Itô processes and discuss in particular when and how they become, upon randomisation, ‘doubly stochastic’ Itô processes, and what can be said about their conditional laws.