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, for which a robust approach named binary population synthesis (BPS) warrants special attention. This approach has seen widespread application 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.

双星相互作用导致有趣物体的形成，例如致密双星、超新星、伽马射线爆发、X 射线双星、脉冲星、新星、灾难性变星、热亚矮星、钡星和蓝色落伍者。为了研究二元种群的演化以及这些天体的后续形成，多年来已经开发了许多方法，其中一种称为二元种群合成 (BPS) 的稳健方法值得特别关注。这种方法已在天体物理学的许多领域得到广泛应用，包括但不限于对星系恒星含量的分析、星系化学演化研究以及关于恒星形成和宇宙再电离的研究。在这篇评论中，我们讨论了 BPS 的作用、它的总体情况以及构成它的各种组件。我们特别关注二元质量传递的稳定性标准，因为这种稳定性在很大程度上决定了二元系统的命运。我们以我们对该领域未来的看法结束。