Abstract I will present results from a large extragalactic CO, 13CO and HCN multi-J line survey of Luminous Infrared Galaxies conducted with the James Clerk Maxwell Telescope (JCMT) in Hawaii (USA), the IRAM 30-m telescope in Granada (Spain), and expanded in Space using the Herschel Space Observatory (HSO). Analysis of complete CO Spectral Line Energy Distributions J=1--0 up to J=13--12 and the rest of the molecular lines strongly points to two major paradigm shifts: 1) Photon-dominated Regions (PDRs) are not the main power source of high-J CO line emission in (U)LIRGs (Ultra-luminous LIRGs with L_IR>10^{11} Lsol) nor they are the main repository of their molecular gas mass 2) The low-J CO lines are inappropriate to obtain the total molecular gas or to discern the star formation mode of LIRGs (merger versus disk). A serious implication is the underestimate of the H2 mass in LIRGs by up to factors of 5.