Star formation is a key physical process of baryonic matters, and plays crucial roles in driving galaxy formation and evolution. The observed relationship between star formation rates and gas masses offers a powerful empirical way in understanding star formation and is widely invoked in numerical simulations of galaxy formation and evolution. In the past decade, the rich multi-wavelength data of nearby galaxies have enabled well characterizations of this gas-SFR relationship. However, the majority of these works focuses on studies of galaxies that are typical in the local universe but may be largely different from those in the early Universe. In this talk, I will represent our recent works along with others’ that probe star formation in some extreme environments such as galaxy outer disks, extreme low metallicity galaxies, mergers etc. All these works challenge the traditional SFR-gas relationship, implying that different physical mechanisms may play roles in star formation during galaxy evolution.