Dietary fatty acids (FA) consumed by sheep, like other ruminants, can undergo biohydrogenation resulting in high proportions of saturated FA (SFA) in meat. Biohydrogenation is typically less extensive in sheep than cattle, and consequently, sheep meat can contain higher proportions of omega (n)− 3 polyunsaturated FA (PUFA), and PUFA biohydrogenation intermediates (PUFA-BHI) including conjugated linoleic acid (CLA) and trans-monounsaturated FAs (t-MUFA). Sheep meat is also noted for having characteristically higher contents of branched chain FA (BCFA). From a human health and wellness perspective, some SFA and trans-MUFA have been found to negatively affect blood lipid profiles, and are associated with increased risk of cardiovascular disease (CVD). On the other hand, n − 3 PUFA, BCFA and some PUFA-BHI may have many potential beneficial effects on human health and wellbeing. In particular, vaccenic acid (VA), rumenic acid (RA) and BCFA may have potential for protecting against cancer and inflammatory disorders among other human health benefits. Several innovative strategies have been evaluated for their potential to enrich sheep meat with FA which may have human health benefits. To this end, dietary manipulation has been found to be the most effective strategy of improving the FA profile of sheep meat. However, there is a missing link between the FA profile of sheep meat, human consumption patterns of sheep FA and chronic diseases. The current review provides an overview of the nutritional strategies used to enhance the FA profile of sheep meat for human consumption.