Since low-back pain is increasing in ageing populations, current research efforts are focused on obtaining a better understanding of the pathophysiology of intervertebral disc degeneration and on developing new therapeutic strategies. This requires adequate and clinically relevant models of the disease process. Ex vivo models can provide insights into isolated aspects of the degenerative/regenerative processes involved; although, ultimately, in vivo models are needed for preclinical translational studies. Such models have been developed in numerous animal species with significant variations in size and disc physiology and their number is considerable. Importantly, the choice of the model has to be tailored to the aim of the study. Given the number of available options, it is important to have a good understanding of the various models of disc degeneration and to be fully aware of their advantages and limitations. After comparing the anatomy and histology of intervertebral discs in animals and humans, the present study provides an overview of the different models of in vivo disc degeneration. It also provides a comprehensive guide with suggested criteria to select the most appropriate animal model in a question-driven manner.