The intervertebral disc (IVD) provides flexibility, acts as a shock absorber, and transmits load. Degeneration of the IVD includes alterations in the biomechanics, extracellular matrix (ECM), and cellular activity. These changes are not always perceived, however, IVD degeneration can lead to severe health problems including long-term disability. To understand the pathogenesis of IVD degeneration and suitable testing methods for emerging treatments and therapies, this review documents in-vitro models of IVD degeneration including physical disruption, hyperphysiological loading, ECM degradation by enzyme digestion, or a combination of these methods. This paper reviews and critically analyses the models of degeneration published since the year 2000 in either in human or animal specimens. The results are categorised in terms of the IVD biomechanics, physical attributes, ECM composition, tissue damage and cellularity to evaluate the models with respect to natural human degeneration, and to provide recommendations for clinically relevant models for the various stages of degeneration. There is no one model that replicates the wide range of degenerative changes that occur as part of normal degeneration. However, cyclic overloading replicates many aspects of degeneration, with the advantage of a dose-response allowing the tuning of damage initiated. Models of severe degeneration are currently lacking, but there is potential that combining cyclic overloading and enzymatic digestion will provide model that closely resembles human IVD degeneration. This will provide an effective way to investigate the effects of severe degeneration, and the evaluation of treatments for the IVD, which would generally be indicated at this advanced stage of degeneration.