Luminous Compact Blue Galaxies (LCBGs) are high surface brightness starburst galaxies bluer than a typical SBc and with typical luminosities ≈ L ⋆, which are undergoing a major burst of star formation. LCBGs are the closest counterparts to the large population of starburst galaxies observed at high redshift, including Lyman-break galaxies at z ≈ 2. However, because LCBGs are very rare in the nearby Universe, their properties are still largely unknown. We have selected a representative sample of LCBGs from the SDSS and UCM databases which, although small, provides an excellent reference for comparison with current and future surveys of similar starbursts at high-z. We are carrying out a 3D optical and radio spectroscopic study of this LCBG sample, including spatially resolved maps of kinematics, extinction, SFR and metallicity. This will allow us to characterize their star formation history and mass assembly, and the role of mergers and supernova galactic winds. Here we show our results of this comprehensive multiwavelength study for NGC 7673, a prototypical LCBG in the nearby Universe.