Animals that accurately model human disease are invaluable in medical research, allowing a critical understanding of disease mechanisms, and the opportunity to evaluate the effect of therapeutic compounds in pre-clinical studies. Many types of animal models are used world-wide, with the most common being small laboratory animals, such as mice. However, rodents often do not faithfully replicate human disease, despite their predominant use in research. This discordancy is due in part to physiological differences, such as body size and longevity. In contrast, large animal models, including sheep, provide an alternative to mice for biomedical research due to their greater physiological parallels with humans. Completion of the full genome sequences of many species, and the advent of Next Generation Sequencing (NGS) technologies, means it is now feasible to screen large populations of domesticated animals for genetic variants that resemble human genetic diseases, and generate models that more accurately model rare human pathologies. In this review, we discuss the notion of using sheep as large animal models, and their advantages in modelling human genetic disease. We exemplify several existing naturally occurring ovine variants in genes that are orthologous to human disease genes, such as the Cln6 sheep model for Batten disease. These, and other sheep models, have contributed significantly to our understanding of the relevant human disease process, in addition to providing opportunities to trial new therapies in animals with similar body and organ size to humans. Therefore sheep are a significant species with respect to the modelling of rare genetic human disease, which we summarize in this review.