Doping of TiO2 is a very active field, with a particularly large effort expended using density functional theory (DFT) to modeldoped TiO2; this interest has arisen from the potential for doping to be used in tuning the band gap ofTiO2 for photocatalytic applications. Doping is also of importance for modifying the reactivity ofan oxide. Finally, dopants can also be unintentionally incorporated into an oxide duringprocessing, giving unexpected electronic properties. To unravel properly how dopingimpacts on the properties of a metal oxide requires a modelling approach that candescribe such systems consistently. Unfortunately, DFT, as used in the majority ofstudies, is not suitable for application here and in many cases cannot even yield aqualitatively consistent description. In this paper we investigate the doping of bulk rutileTiO2 with trivalent cations, Al, Ga and In, using DFT, DFT corrected for on-site Coulomb interactions (DFT + U, withU on oxygen 2p states) and hybrid DFT (the screened exchange HSE06 exchange correlationfunctional) in an effort to better understand the performance of DFT in describing suchfundamental doping scenarios and to analyse the process of charge compensation with thesedopants. With all dopants, DFT delocalizes the oxygen hole polaron that results fromsubstitution of Ti with the lower valence cation. DFT also finds an undistortedgeometry and does not produce the characteristic polaron state in the band gap.DFT + U and hybrid DFT both localize the polaron, and this is accompaniedby a distortion to the structure around the oxygen hole site.DFT + U and HSE06 both give a polaron state in the band gap. The band gap underestimation present inDFT + U means that the offset of the gap state from both the valence and the conductionband cannot be properly described, while the hybrid DFT offsets should becorrect. We have investigated dopant charge compensation by formation ofoxygen vacancies. Due to the large number of calculations required, we useDFT + U for these studies. We find that the most stable oxygen vacancy site has either a very smallpositive formation energy or is negative, so under typical experimental conditions, anionvacancy formation will compensate for the dopant.