Lu3Al5O12 (LuAG) doped with Ce3+ is a promising scintillator material with a high density and a fast response time. The light output under x-ray or y-ray excitation is however well below the theoretical limit. In this paper the influence of co-doping with Tb3+ is investigated with the aim to increase the light output. For singly doped LuAG (with Ce3+ or Tb3+) high resolution spectra are reported giving insight in the energy level structure of the two ions in LuAG. For Ce3+ zero-phonon lines and vibronic structure is observed for thetwo lowest energy d-bands and the Stokes shift (2350 cm-1) and Huang-Rhys coupling parameter (S = 9) have been determined. For Tb3+ transition to the high spin (HS) and low spin (LS) states are observed (including a zero-phonon line and vibrational structure for the highspin state). The HS-LS splitting is 5400 cm-1 which is smaller thanusually observed and is explained by a reduction of the d-f exchangecoupling parameter J by covalency. Upon replacing the smaller Lu3+ion with the larger Tb3+ ion, the crystal field splitting for the lowest d-states increases and the Ce3+ emission shows a redshift, causing the lowest d-state to shift below the 5D4 state of Tb3+ and allowing for efficient energy transfer from Tb3+ to Ce3+ down to the lowest temperatures. Luminescence decay measurements confirm efficientenergy transfer from Tb3+ to Ce3+ and provide a qualitative understanding of the energy transfer process. Co-doping with Tb3+ does not result in the desired increase in light output and an explanation based on electron trapping in defects is discussed.