The interstellar medium (ISM) plays a key role in the star formation history of galaxies. Molecular hydrogen, H2, is the phase of the interstellar medium (ISM) most closely related to star formation. Clouds of molecular gas are thought to be birthplaces of virtually all stars, and H2 often dominates the mass budget of the ISM in the inner, most vigorously star-forming parts of spiral galaxies. Building up on our LABOCA observations of SINGs galaxies, the IRAM 30m CO(2-1) HERACLES sample and HERSCHEL dust continuum observations (KINGFISH) we have studied the star-formation law in nearby galaxies. One of the main results comes from the HERACES survey from which we investigate the star-formation law via stacking techniques in the HI dominated outskirts of nearby galaxies. We show also in these regions the SFR law is “purely a molecular law” with a linear relation between the surface density of molecular gas and star formation. We also investigate the star-formation law in nearby, low metallicity dwarf galaxies. Here LCO per SFR orders of magnitude smaller in dwarf galaxies. One possible interpretation is that dwarf galaxies form stars much more efficiently; we argue that the low LCO/SFR ratio is due to the fact that the CO-to-H2 conversion factor, αCO, changes significantly in low metallicity environments.