The importance of Luminous and Ultraluminous infrared galaxies (U/LIRGs) in the context of the cosmological evolution of the star-formation has been well established in the last decades. They have been detected in large numbers at high-z (z>1) in deep surveys with Spitzer and Herschel, and they seem to be the dominant component to the star formation rate (SFR) density of the Universe beyond z~2. Although rare locally, nearby U/LIRGs are valuable candidates to study extreme cases of compact star-formation and coeval AGN. In particular, the study of local U/LIRGs using near-IR integral field spectroscopic techniques allows us to disentangle the 2D distribution of the gas and the star-formation using high spatial resolution, and characterise dust-enshrouded, spatially-resolved star-forming regions with great amount of detail. In that context, we are carrying on a comprehensive 2D IFS near-IR survey of local 10 LIRGs and 12 ULIRGs, based on VLT-SINFONI observations. I will review different topics on the spatially resolved study of the ISM and the star-formation at different spatial scales. I will focus on the analysis of the multi-phase gas morphology and kinematics, and on the study of the spatially-resolved distribution of the extinction-corrected star-formation rate (SFR) and star-formation rate surface density (ΣSFR). In particular, I will present some recent results on the characterization of individual star-forming regions, in terms of their sizes and Paα luminosities.