Stars including our Sun are born in clouds of cold gas. Understanding how gas converts into stars across cosmic time is a big challenge in modern astronomy. In the early universe, primordial gas with little or no metals collapse into early-generation stars whose radiation re- ionizes the universe. The subsequent rising of the cosmic star-formation-rate (SFR) density until z∼2 follows by a rapid decline toward the current universe. The driving mechanism of this cosmic SFR evolution is related to the cold gas reservoir available within the galaxies and its capability of forming new stars. In this talk, I will review recent progresses including our own works in understanding the evolution of cosmic star formation, with the focus on answering three key questions: how does cosmic star formation start, how does cosmic star formation evolve, and how does star formation stop?