We describe a next major frontier in observational studies of galaxy evolution and star formation: linking the physical conditions in the cold, star-forming interstellar medium to host galaxy and local environment. The integrated gas content of galaxies has been surveyed extensively over the last decades. The link between environment and cold gas density, turbulence, excitation, dynamical state, and chemical makeup remain far less well understood. We know that these properties do vary dramatically and theoretical work posits a strong connection between the state of the gas, its ability to form stars, and the impact of stellar feedback. A next major step in the field will be to use sensitive cm-, mm-, and submm-wave spectroscopy and high resolution spectroscopic imaging to survey the state of cold gas across the whole local galaxy population. Such observations have pushed the capabilities of the current generation of telescopes. We highlight three critical elements for progress in the next decade: (1) robust support and aggressive development of ALMA, (2) the deployment of very large heterodyne receiver arrays on single dish telescopes, and (3) development of a new interferometric array that dramatically improves on current capabilities at cm- and mm-wavelengths (~ 1-115 GHz).
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