Abstract：I will present our analysis results on the mid-J CO line emission over galaxy scale from a large sample of local luminous infrared galaxies (LIRGs) observed with Herschel Space Observatory and the CO (6-5) line emission over a scale of 30-100 pc in the nuclei of representative LIRGs observed with ALMA. The mid-J CO line emission acts as the cooling mechanism for the dense molecular gas that is giving birth to and also receiving energetic feedback from young stars. I will highlight what we have learnt from these observations with respect to the interplay between molecular gas, star formation and AGN, and illustrate how one can apply our local knowledge to characterizing star formation and gas properties in high-z galaxies.