Connecting the density structure of molecular clouds with star formation

In the current paradigm of turbulence-regulated interstellar medium (ISM), star formation rates of entire galaxies are intricately linked to the density structure of the individual molecular clouds. This density structure is essentially encapsulated in the probability distribution function of volume densities (ρ-PDF), which directly affects the star formation rates predicted by analytic models. Contrasting its fundamental role, the ρ-PDF function has remained virtually unconstrained by observations. I describe in this contribution the recent progress in attaining observational constraints for the column density PDFs (N-PDFs) of molecular clouds that function as a proxy of the ρ-PDFs. Specifically, observational works point towards a universal correlation between the shape of the N-PDFs and star formation activity in molecular clouds. The correlation is in place from the scales of a parsec up to the scales of entire galaxies, making it a fundamental, global link between the ISM structure and star formation.