Sheep meat is consumed and appreciated all over the world for its nutritional value and flavor. However, this meat is very perishable and easily subjected to the action of both spoilage and pathogenic microorganisms. For this reason, in combination with cold storage, effective preservation techniques are required. There is increasing interest in the application of natural antimicrobials, such as essential oils, extracts, spices, and by-products of the food industry. This review analyses the studies on natural antimicrobials in sheep meat and sheep meat products and gathers evidence about the encouraging results achieved on the reduction and/or elimination of spoilage and pathogenic microorganisms. The use of these natural antimicrobial alternatives might open up important perspectives for industrial application, considering that this specific meat is often traded over long distances. In fact, on the basis of scientific literature, natural antimicrobials can be considered a sustainable and affordable alternative to extend the shelf life of sheep meat and guarantee its safety, although many factors need to be further investigated, such as the sensory impact, potential toxicity, and economic aspects. For all these issues, investigated in some of the studies reviewed here, it is fundamental to obtain the antimicrobial effect with the minimum amount of effective substance to avoid sensory modifications, toxic effects, and unbearable costs. This study sets foundations for the possible direction of future studies, which will contribute to identify effective solutions for industrial applications of natural antimicrobials in the sheep meat industry.