Mass accretion is a main driver for the evolution of disks around young low-mass stellar objects (YSOs). Observationally, the study of accretion in YSOs is conducted via multi-wavelength observations, and our JEDI group has been very active in investigating classical T Tauri stars (CTTS), young (a few Myr), very low- to solar-mass stars that are actively accreting mass from planet-forming disks. The evolution of disk mass accretion , from the early proto-stellar phase to the proto-planetary disk dispersal is addressed through optical/IR spectroscopic surveys with different facilities (e.g. X-shooter, UVES, KMOS at VLT, GIARPS at TNG). Accretion properties of stars in young clusters having different environments and metallicity (outer galaxy and MC) are also studied and will be in particular addressed in the near future through GTO programs at VLT/MOONS and JWST, and through dedicated surveys. We also address variability due to accretion bursts, thanks in particular to the participation of JEDI members to the Rubin-LSST surveys.