Quantum ESPRESSO is an open-source distribution of computer codes for quantum-mechanical materials modeling, based on density-functional theory, pseudopotentials, and plane waves, and renowned for its performance on a wide range of hardware architectures, from laptops to massively parallel computers, as well as for the breadth of its applications. In this paper, we present a motivation and brief review of the ongoing effort to port Quantum ESPRESSO onto heterogeneous architectures based on hardware accelerators, which will overcome the energy constraints that are currently hindering the way toward exascale computing.