AstroSat, a dedicated Space Observatory of India, has completed five successful years of operation in space on 28th September 2020. AstroSat is a quite complex satellite, as it is a multi-wavelength observatory with many scientific instruments. The saga of many agencies, including Indian Space Research Organisation, the lead agency, and many scientists and engineers has resulted in realizing and operating this mission with excellent performance and highly satisfactory results. This mission generated a lot of observations leading to enhanced research activity for Indian astronomers, as well as international astronomers. It has also kindled interest, as expected, in young scientists and science students. The mission still continues in orbit contributing to celestial observations. AstroSat is a collaborative effort of many agencies not only from India but also from international agencies. The managers and the project team had to face many technological and managerial challenges at various stages of the mission. In this paper we present the challenges in conceiving a space science mission in India, and methods adopted to overcome them to make the mission successful. This may help in planning and executing future space science missions, more efficiently, meeting the growing demands from the scientific community involved in the frontier areas of space research.