The role of transition-metal impurities in Yb3+-doped YLiF4 (YLF) laser-cooling crystals is studied. Divalent 3d transition-metal ions, in particular Fe2+, are found to have strong absorptions at the laser cooling pump wavelength and degrade the cooling efficiency by introducing background absorption. A set of eight substitutional and chargecompensated defects that form upon introduction of 1+, 2+, and 3+ transition-metal ions into the YLF crystal lattice is proposed. A calculation of solution energies for each defect type and for a range of 3d ions is carried out. It indicates that divalent 3d ions preferentially substitute for Y3+ accompanied by a fluoride vacancy for charge compensation. An electron paramagnetic resonance (EPR) study of a YLF crystal identifies Fe2+ in the crystal lattice, in agreement with the elemental analysis and the computational results. A strategy for purifying the YF3, LiF, and YbF3 starting materials for the YLF:Yb crystal growth is discussed. Chelate-assisted solvent extraction purification with pyrrolidine dithiocarbamate (APDC) for Y, Li, and Yb as well as ethylenediaminetetraacetic acid (EDTA) for Li was carried out.