Understanding defects in amorphous oxide films and heterostructures is vital to improving performance of microelectronic devices, thin-film transistors, and electrocatalysis. However, to what extent the structure and properties of point defects in amorphous solids are similar to those in the crystalline phase are still debated. The validity of this analogy and the experimental and theoretical evidence of the effects of oxygen deficiency in amorphous oxide films are critically discussed. The authors start with the meaning and significance of defect models, such as "oxygen vacancy" in crystalline oxides, and then introduce experimental and computational methods used to study intrinsic defects in amorphous oxides and discuss their limitations and challenges. To test the validity of existing defect models, ab initio molecular dynamics is used with a non-local density functional to model the structure and electronic properties of oxygen-deficient amorphous alumina. Unlike some previous studies, the formation of deep defect states in the bandgap caused by the oxygen deficiency is found. Apart from atomistic structures analogous to crystal vacancies, the formation of more stable defect states characterized by the bond formation between under-coordinated Al ions is shown. The limitations of such defect models and how they may be overcome in simulations are discussed.