Sesame (Sesamum indicum L.), also called simsim, benne, or gingelly, is one of the oldest cultivated oilseed crops grown for the extraction of edible oil. Although its origin is contested, it most likely originates in Asia (probably India) or eastern Africa. Sesame tolerates hot and dry conditions and grows when other crops fail. Sesame seeds have one of the highest oil contents of any seed; 37% to 63% depending on the cultivar and growing season. There has been an increase in the demand for sesame in international markets, largely due to its nutritious properties and its inclusion in a variety of foods. Despite its nutritional and high-value attributes, as well as increased demand in international markets, sesame is still an orphan crop. There is no international agricultural research center with a research mandate for sesame; consequently, the crop has attracted limited scientific research. Sesame is widely grown in warmer regions of the world, with the largest production occurring in Africa and Asia; the major producing countries include Sudan, India, Myanmar, Tanzania, Nigeria and China. In Africa, sesame is mainly grown in the northern and western regions. The crop receives little support from researchers, industry, or policymakers; as a result, it lags behind other oilseed crops in terms of genetic advancement. Its production in Africa is mainly carried out by small-scale farmers; there is minimal use of inputs, such as fertilizers and other agrochemicals. Farmers plant low-yielding local varieties and obtain seeds from informal sources, especially own-saved seeds. There are also huge pre- and post-harvest losses, especially from uneven shattering of capsules. This review looks into sesame production systems in Africa and the constraints encountered by various producers in different countries. The identified constraints might provide a basis for implementing practical and profitable interventions to enhance sesame production in Africa. Deliberate efforts should be made to improve sesame production; the crop needs policy and research attention if high production is to be achieved.