Noisy Intermediate-Scale Quantum (NISQ) computers promise to perform computations beyond the reach of modern computers with far-reaching implications for scientific research. Due to remarkable technological advances, small scale devices are now becoming available for use. There has recently been a flurry of proof-of-principle experiments and many exciting theoretical proposals about how to use NISQ to simulate quantum many-body systems in and out of equilibrium. Current applications range from the simulation of far out-of-equilibrium dynamics to the study of topological phases of matter. This Focus Workshop aims to give an overview of recent theoretical and experimental developments within this young field and point towards the open questions.