Despite the importance of maize as a staple crop in Southern Africa, production remains subdued, averaging 1 tha−1 under smallholder farming systems. Although the low yields can be attributed to several biotic (e.g., pests and diseases) and abiotic (e.g., infertile soils) phenomenon, the climate change-induced abiotic stresses (in particular, heat and drought) are regarded as the major constrains threatening maize productivity, globally. Since climatic models are predicting exacerbated incidences of drought and heat stress, societies that depend on maize for survival will also be at risk if plant breeders lose focus in developing varieties productive under these predicted climatic scenarios. In this review, we provide: (1) a summary of the known effects of drought and heat stress on maize production, (2) a summation of the morpho-physiological adaptation mechanisms of maize to heat and drought as well as (3) a summary of strides made on the molecular front in understanding how heat and drought stress tolerance/resistance in maize is genetically controlled. We hypothesize that a better understanding of how heat and drought stress impacts of maize productivity, together with a deeper appreciation of mechanisms employed by maize germplasm tolerant/resistant to the stress conditions, can guide maize breeders in structuring a holistic program for developing maize varieties productive under these abiotic stresses.