Star formation is among the most complex processes studied by astronomers to date. It is characterised by a multi-scale interplay between gravity, turbulence, magnetic field, galactic shear as well as ironizing radiation. Because of its complexity, the physical mechanisms that drive the star formation remain unclear.I will present a few recent advancements. First, I present results from our recent study in the Galactic Center region, where, because of its unique location, shear can drastically reduce the star formation efficiency. I will present our study on the fragmentation of gas clouds, and provided evidences where turbulence have supported against fragmentation. Finally, I argue that due to the complexity, it is necessary to develop mathematical tools to analyse the structures, and will present one example.