The next 15 years promise a revolution in our understanding of the formation and evolution of compact objects in binary systems. Observations across both the electromagnetic (EM) and gravitational wave (GW) spectrums will allow characterizations of compact objects and their progenitors during several stages of binary star evolution. The interpretation of these observations relies on a theoretical understanding of how different physical processes that occur during binary star evolution are imprinted on the observable population. In this talk I will introduce a recently developed binary population synthesis code, COSMIC, designed to simulate realistic Milky Way populations of binary stars using recent models for binary star interactions and compact object formation. I will also highlight recent work which uses cosmic to show how EM and GW observations can be used to gain insight into the formation and evolution of compact object populations from close double white dwarf binaries to wide black hole binaries.