Cold gas is the raw material for star formation (SF) in galaxies. Owing to gravitational force, cold gas collapses into dense molecular cloud cores and will eventually continue to collapse and transform into stars. Moreover, SF feedback drives the formation and evolution of galaxies. A detailed understanding of the properties of molecular gas, the description of the physical relationship between SF and galaxies, and SF feedback in galaxies are extremely important studies today. Herein, we only summarize the physical laws of SF in extragalactic galaxies and discuss the relationship between SF and cold gas. In particular, with further physical understanding of star formation, we will summarize our series of related studies on the relationship between SF and dense molecular gas. From the overall global study of entire galaxies, distant external galaxies, and the spatially resolved decomposition of nearby galaxies down to the Galactic dense cloud cores, the linear relationship is valid with a span of 10 orders of magnitude. At even higher densities traced by higher- J rotation ladders of dense gas tracers, this 10-orders-of-magnitude correlation is again tightly maintained from entire galaxies to the spatial decomposition of the denser gas in nearby galaxies, spanning further with the Galactic dense cloud cores. We further discuss future development prospects of this research direction in the Atacama Large Millimeter/submillimeter Array (ALMA) era. The James Clerk Maxwell Telescope large project MALATANG provides an understanding of the large-scale distribution of extremely dense and warm molecular gas in nearby galaxies and probes the relationships among the various gas phases, the dense molecular gas, and SF in the centers of the galaxies and most of the inner spiral disks, ultimately elucidating the physical connection in the relationship between SF and dense molecular gas on different physical scales. With the advancement of ALMA/NOrthern Extended Millimeter Array observations and the investment in next-generation telescopes, we expect to finally obtain the physical properties and laws of dense molecular gas and SF on different physical scales, from the molecular cloud scale to different regions in galaxies (distant and/or nearby galaxies). Eventually, a breakthrough understanding of contemporary issues, such as multispectral diagnosis and local SF efficiency of galaxies, will be in sight.