Separations of mixtures play a critical role in chemical industries. Over the last century, the knowledge in the area of chemical thermodynamics and modeling of separation processes has been substantially expanded. Since the models are still not completely accurate, hybrid models can be used as an alternative that allows to retain existing knowledge and augment it using data. This paper explores some of the weaknesses in the current knowledge in separations design, simulation, optimization, and operation, and presents many examples where data-driven and hybrid models have been used to facilitate these tasks.