In the local universe, galaxies fall into one of two populations: a star-forming blue cloud and a red sequence lacking star formation. At redshift z ~ 1.5, however, the red sequence has yet to develop. Over the past 9 Gyrs some process has quenched star formation in blue galaxies and caused them to evolve onto the red sequence by fading and/or merging of their stellar populations. While such a transformation may be occurring across the full range of masses, the highest rate of evolution occurs in massive starbursts at the luminous end of the blue cloud. These galaxies are the Luminous Compact Blue Galaxies (LCBGs). In this talk I present preliminary results of a comprehensive multiwavelength survey of LCBGs from z ~ 0 to z ~ 3 we will be carrying out over the next 5 years using several space and ground-based observatories, including the GTC.