The astrodynamics software is a bridge between the astrodynamics theory and the engineering application, which can evidently improve the e-ciency and the ability of the space mission design and analysis. There are many mature software systems in the world, but many of them are not available in our country. In recent years, great progress has been made in the fleld of the national astrodynamics research and the engineering applications, but the mature astrodynamics software remains almost a blank area. The development of the international astrodynamics software is surveyed and sorted into two kinds:the space mission analysis and the spacecraft trajectory optimization. The representative open-source and commercial software systems are introduced, including JAT, STK, Freeflyer, POST and ASTOS. Additionally, the development of the Chinese astrodynamics software is also reviewed. At last, the technical characteristics of difierent astrodynamics softwares are summarized, and preliminary suggestions for the development of a mature astrodynamics software in China are given.