A next main step in understanding star formation is to link the sharp but narrow view of Galactic molecular cloud studies to the wider context accessed by less detail by extragalactic work. In this proceeding, we discuss how new technology and large programs at millimeter wavelengths are improving our ability to access physical conditions in the interstellar medium (ISM) of other galaxies. We highlight results from the multi-line survey of Usero et al. (2015), which measured density sensitive lines across nearby galaxy disks, and two new mapping studies of M51: the high resolution Plateau de Bure Arcsecond Whirlpool Survey (PAWS) and the EMPIRE multi-line mapping survey. These results argue for a context-dependent role for gas density in star formation; that is, gas at a particular density does not appear to form stars in a universal way. They also demonstrate the influence of cloud-scale conditions, especially surface density and the velocity dispersion, in setting the small-scale density distribution and highlight gravitational boundedness as a main driver of the ability of gas to form stars. Beyond these specific results, we argue that ability to gauge detailed physical conditions in the star-forming gas of other galaxies promises major advances that will help unify the fields of Galactic and extragalactic star formation in the next few years.