Recent high resolution interferometric observations of the molecular gas in luminous IR galaxies reveal extraordinary concentrations of star forming material in the central few kpc. In several of the nearest IR bright galaxies, the molecular gas in the central regions is concentrated in a bar-like distribution (IC342, NGC 6946, and NGC 253) and in NGC 1068, approximately 40% of the molecular gas is confined to two arms or a ring at approximately 1.6 kpc radius. Interferometry on the most luminous galaxies (LIR ≥ 1011L⊙) reveals that approximately half of the total interstellar matter is contained in the central kpc with mean densities of several hundred H2 cm-3. Such gas concentrations should result in the very rapid formation of stars, i.e. a central star burst yielding a massive central star cluster.