  Binary interactions lead to the formation of intriguing objects, such as
compact binaries, supernovae, gamma ray bursts, X-ray binaries, pulsars, novae,
cataclysmic variables, hot subdwarf stars, barium stars, and blue stragglers.
To study the evolution of binary populations and the consequent formation of
these objects, many methods have been developed over the years, of which a
robust approach named binary population synthesis (BPS) warrants special
attention. This approach has seen widespread use in many areas of astrophysics,
including but not limited to analyses of the stellar content of galaxies,
research on galactic chemical evolution, and studies concerning star formation
and cosmic re-ionization. In this review, we discuss the role of BPS, its
general picture, and the various components that comprise it. We pay special
attention to the stability criteria for mass transfer in binaries, as this
stability largely determines the fate of binary systems. We conclude with our
perspectives regarding the future of this field.
