Binary stars are as common as single stars. Binary stars are of immense importance to astrophysicists because that they allow us to determine the masses of the stars independent of their distances. They are the cornerstone of the understanding of stellar evolutionary theory and play an essential role in cosmic distance measurement, galactic evolution, nucleosynthesis and the formation of important objects such as cataclysmic variable stars, X-ray binaries, Type Ia supernovae, and gravitational wave-producing double compact objects. In this article, we review the significant theoretical and observational progresses in addressing binary stars in the new millennium. Increasing large survey projects have led to the discovery of enormous numbers of binary stars, which enables us to conduct statistical studies of binary populations, and therefore provide unprecedented insight into the stellar and binary evolution physics. Meanwhile, the rapid development of theoretical concepts and numerical approaches for binary evolution have made a substantial progress on the alleviation of some long-standing binary-related problems such as the stability of mass transfer and common envelope evolution. Nevertheless, it remains a challenge to have a full understanding of fundamental problems of stellar and binary astrophysics. The upcoming massive survey projects and increasingly sophisticated computational methods will lead to future progress.

双星与单星一样常见。双星对于天体物理学家来说非常重要，因为它们使我们能够确定恒星的质量，而与它们的距离无关。它们是理解恒星演化理论的基石，在宇宙距离测量、星系演化、核合成以及灾变变星、X射线双星、Ia型超新星和引力波等重要天体的形成中发挥着至关重要的作用。产生双紧凑物体。在本文中，我们回顾了新千年解决双星问题的重大理论和观测进展。越来越多的大型调查项目导致了大量双星的发现，这使我们能够对双星种群进行统计研究，从而为恒星和双星演化物理学提供前所未有的见解。与此同时，二元演化理论概念和数值方法的快速发展，在解决一些长期存在的二元相关问题，如传质稳定性和共同包络演化等方面取得了实质性进展。然而，充分理解恒星和双星天体物理学的基本问题仍然是一个挑战。即将到来的大规模调查项目和日益复杂的计算方法将带来未来的进展。