The interstellar medium of galaxies is composed of multiple phases, including molecular, atomic, and ionized gas, as well as dust. Stars are formed within this medium from cold molecular gas clouds, which collapse due to their gravitational attraction. Throughout their life, stars emit strong radiation fields and stellar winds, and they can also explode as supernovae at the end of their life. These processes contribute to stirring the turbulent interstellar medium and regulate star formation by heating up, ionizing, and expelling part of the gas. However, star formation does not proceed uniformly throughout the history of the Universe and decrease by an order of magnitude in the last ten billion years. To understand this winding-down of star formation and assess possible variations in the efficiency of star formation, it is crucial to probe the molecular gas reservoirs from which stars are formed. In this article following my presentation at the 10th International Conference on Frontiers of Plasma Physics and Technology held in Kathmandu from 13–17 March 2023, I review some aspects of the multiphase interstellar medium and star formation, with an emphasis on the interplay between neutral and ionized phases, and present recent and ongoing observations of the molecular gas content in typical star-forming galaxies across cosmic time and in different environments. I also present some of our understanding of star-forming galaxies from theoretical models and simulations.