Climate change is shifting agricultural production, which could impact the economic and cultural contexts of the oilseed industry, including sesame. Environmental threats (biotic and abiotic stresses) affect sesame production and thus yield (especially oil content). However, few studies have investigated the genetic enhancement, quality improvement, or the underlying mechanisms of stress tolerance in sesame. This study reveals the challenges faced by farmers/researchers growing sesame crops and the potential genetic and genomic resources for addressing the threats, including: (1) developing sesame varieties that tolerate phyllody, root rot disease, and waterlogging; (2) investigating beneficial agro-morphological traits, such as determinate growth, prostrate habit, and delayed response to seed shattering; (3) using wild relatives of sesame for wide hybridization; and (4) advancing existing strategies to maintain sesame production under changing climatic conditions. Future research programs need to add technologies and develop the best research strategies for economic and sustainable development.