We review recent observations of molecular gas in nearby galaxies and their implications for the star formation law on large (> 1 kpc) scales. High-resolution data provided by millimetre interferometers are now adding to the basic understanding that has been provided by single-dish telescopes. In particular, they confirm the good correlation between star formation rate (SFR) and molecular gas surface densities, while at the same time revealing a greater degree of heterogeneity in the CO distribution. Galaxies classified as SAB or SB tend to show radial CO profiles that peak sharply in the inner ∼20″, indicative of bar-driven inflow. The observed Schmidt law index of ≍1.5 may result from a nearly linear relation between SFR and H2 mass coupled with a modest dependence of the molecular gas fraction on the total gas density. The normalisation of the Schmidt law, giving the characteristic timescale for star formation, may stem from the generic nature of interstellar turbulence.