A substantial fraction of cosmic star formation happens in star clusters, and binary populations residing in extreme cluster environments are fundamentally different from those in galactic fields. Each binary in a star cluster will evolve through a multitude of interactions with other cluster members. A better understanding of this evolution is required to answer some of the most pressing questions in modern astrophysics, from the origin of black-hole mergers to the characterization of galaxies in the early Universe. Historically, star clusters have always been cornerstones for our knowledge of stellar evolution. With this workshop, we aim to continue this legacy by establishing them as cosmic probes for binary studies. The workshop intersects four main fields of modern astrophysics: star formation, stellar and binary evolution, star clusters and their dynamics, and gravitational wave astronomy. With this scientific overlap, the workshop wants to bring scientists of all of these fields together and facilitate the scientific exchange that will lead to new insights and scientific breakthroughs.