This seminar will present recent advances on the manybody physics of open quantum systems, an emerging field that is being explored in condensed matter, atomic and optical platforms as well as superconducting quantum circuits. A pedagogical introduction will outline the state-of-the-art theoretical framework and methods, focusing on the competition between strong interactions and dissipation/decoherence. We will review unconventional aspects of dissipative phase transitions and reservoir engineering protocols for the realization of non-trivial phases. We will show how the concepts developed in this context can also be applied to the field of quantum information with noisy intermediate-scale quantum devices.