Physical Conditions in the ISM and the Star Formation-H2 Connection Stunning leaps in data quality over the last decade have revealed important variations in how stars form out of gas across the universe. With the next generation of telescopes and surveys, it is now becoming possible to move beyond bulk correlations to ask: how do conditions within the molecular gas drive the ability of that gas to form stars and how do these conditions depend on galactic environment? I will review several aspects of this topic including the role of dense gas, as traced by high effective density molecules like HCN and HCO+, and the link between the properties of individual molecular clouds and star formation. I will highlight results from the IRAM large program PAWS, the pilot for the new EMPIRE large program, and a new survey of HCN and HCO+ in the disks of normal spiral galaxies. I will also discuss the connection to recent Milky Way results and how observations with new facilities like ALMA and MUSE can help us take the next step in understanding the physics of gas and star formation in galaxies.