Oil palm crops are the most important determinant of the agricultural economy within the segment of oilseed crops. Oil palm growing in their natural habitats are often challenged simultaneously by multiple stress factors, both abiotic and biotic that limit crop productivity and are major constraints to meeting global food demands. The stress-tolerant oil palm crops that mitigate the effects of abiotic stresses on crop productivity are crucially needed to sustain agricultural production. Basal stem rot threatens the development of the industry, and the key to solving the problem is to breed new oil palm varieties resistant to adversity. This has created a need for genetic improvement which involves evaluation of germplasm, pest and disease resistance, earliness and shattering resistance, quality of oil, varieties for different climatic conditions, etc. In recent years, insights into physiology, molecular biology, and genetics have significantly enhanced our understanding of oil palm response towards such stimuli as well as the reason for varietal diversity in tolerance. In this review, we explore the research progress, existing problems, and prospects of oil palm stress resistance-based physiological mechanisms of stress tolerance as well as the genes and metabolic pathways that regulate stress response.