  Binary population synthesis is the method by which predictions of varied
observables of stellar populations can be made from theoretical models of
binary stellar evolution. Binary stars have many more possible evolutionary
outcomes compared to single stars and the relative rates of the different
pathways, such as the rates of different supernova types, depend on uncertain
or poorly constrained physics. In this Chapter we describe population
synthesis, outline the major uncertainties and discuss the relevant predictions
for core-collapse supernovae. After we overview single star evolution we
outline the important physical processes that occur in binaries including
Roche-lobe overflow, common-envelope evolution and supernova kicks. We also
discuss how a synthetic stellar population incorporating interacting binaries
can be constructed and how uncertainties, such as the strength of supernova
kicks, affect any predictions. We illustrate the process by comparing
predictions for the stellar populations in two young star clusters. We then
discuss the important predictions from population synthesis for understanding
core-collapse supernovae, their delay-time distribution and their progenitor
stars. Finally we discuss how we can predict the rate of mergers of compact
remnants and thus predict the initial parameters of gravitational wave sources.
