Massive stars are instrumental to many areas of astrophysics, both in the local universe and at high redshift. The last decade has seen growing evidence of extreme multiplicity rates and a for a large fraction of massive stars to interact with a binary companion before their final explosion. Such interaction has drastic consequences for the further evolution and final fate of both components. However, the exploration of these effects on entire stellar populations, nearby and at high redshift, and on their observational diagnostics, is still in its infancy. With this Lorentz Workshop@Oort, we aim to bridge the gap between the massive stars and extragalactic communities and explore how binarity affects the role of massive stars as Cosmic Engines and as Cosmic Probes in modern astrophysics. During this week, we will review the latest observational and theoretical advances and identify critical areas where progress is desirable.