Recent observations of binary black hole and binary neutron star mergers have ignited interest in the formation and evolution of compact-object binary systems. However, by the time a compact-object binary merges and produces gravitational-wave/electromagnetic signals we can observe, much of the evolutionary history of the stellar progenitors is washed away. By combining binary population synthesis simulations with observations, we can constrain the uncertain processes that govern the evolution of binary stars from zero age main sequence through to compact object formation. In this talk I will introduce an openly developed population synthesis code: COSMIC and highlight some recent work which explores how to combine binary population simulations with future data from gravitational wave and electromagnetic surveys to constrain the formation and evolution of compact-object binaries.