It has been found that a substantial fraction of the total luminosity output from galaxies at high redshift (z>1) emerges at mid- to far-infrared wavelengths. Much of the star formation and AGN activity associated with galaxy building at these epochs appears to reside in a class of luminous infrared galaxies, which emit bulk of their bolometric luminosity at infrared wavelengths. They are often show spectacular morphology resulted from galaxy merger, but are also so heavily enshrouded in dust that a multi-wavelength approach, particularly with penetrating infrared and X-ray observations, would merit in understanding the true nature of this class of objects. The multi-wavelength project "GOALS" for studying the most luminous local infrared galaxies will be outlined and primarily the results from the X-ray component of this project using the Chandra X-ray Observatory will be reviewed.