Ferroelectric interfacial devices consist of materials systems whose interfacial electronic properties (such as a 2D electron gas or an interfacial magnetic spin configuration) are modulated by a ferroelectric layer set in its immediate vicinity. While the prototypical example of such a system is the ferroelectric field effect transistor first proposed in the 1950s, only with the recent advances in the controlled growth of epitaxial thin films and heterostructures, and the recent physical understanding down to the atomic scale of screening processes at ferroelectric-semiconducting and -metallic interfaces made possible by first principles calculations, have the conditions been met for a full development of the field. In this review, we discuss the recent advances in ferroelectric interfacial systems with emphasis on the ferroelectric control of the electronic properties of interfacial devices with well ordered (epitaxial) interfaces. In particular, we consider the cases of ferroelectric interfacial systems aimed at controlling the correlated state, including superconductivity, Mott metallic-insulator transition, magnetism, charge, and orbital order, and charge and spin transport across ferroelectric tunnel junctions. The focus is on the basic physical mechanisms underlying the emergence of interfacial effects, the nature of the ferroelectric control of the electronic state, and the role of extreme electric field gradients at the interface in giving rise to new physical phenomena. Such understanding is key to the development of ferroelectric interfacial systems with characteristics suitable for next generation electronic devices based on controlling the correlated state of matter.