Luminous Compact Blue Galaxies (LCBGs) are high surface brightness starburst galaxies bluer than a typical SBc and brighter than ~ 0.25L*, which are undergoing a major burst of star formation. LCBGs are the closest counterparts of the numerous population of starburst galaxies observed at high redshift, including Lyman-break galaxies at z ~ 2. LCBGs in the nearby universe hold the key to understanding the nature and evolution of the distant population and their evolution into today’s galaxy population. However, because LCBGs are very rare in the nearby universe, their properties are still largely unknown. We have selected a representative sample of LCBGs in the local universe from the SDSS, UCM and MRK catalogs which, although small, provides an excellent reference for comparison with current and future surveys of similar starburst at high redshift. We are carrying out a multiwavelength study of this sample, including 3D optical spectroscopy (PPAK), radio (VLA/GMRT), and NUV and FUV (GALEX).