The population of Africa will double in the next 33 years to reach 2.5 billion by 2050. Although roughly 60% of the continent’s population is engaged in agriculture, the produce from this sector cannot feed its citizens. Hence, in 2013 alone, Africa imported 56.5 million tons of wheat, maize, and soybean at the cost of 18.8 billion USD. Although crops cultivated in Africa play a vital role in their contribution to Food Security, they produce inferior yields compared to those in other parts of the world. For instance, the average cereal yield in Africa is only 1.6 t·ha−1 compared to the global 3.9 t·ha−1. Low productivity in Africa is also related to poor soil fertility and scarce moisture, as well as a variety of insect pests, diseases, and weeds. While moisture scarcity is responsible for up to 60% of yield losses in some African staple cereals, insect pests inflict annually substantial crop losses. In order to devise a strategy towards boosting crop productivity on the continent where food insecurity is most prevalent, these production constraints should be investigated and properly addressed. This review focuses on conventional (also known as genetic) intensification in which crop productivity is raised through breeding for cultivars with high yield-potential and those that thrive well under diverse and extreme environmental conditions. Improved crop varieties alone do not boost crop productivity unless supplemented with optimum soil, water, and plant management practices as well as the promotion of policies pertaining to inputs, credit, extension, and marketing. Studies in Kenya and Uganda have shown that the yield of cassava can be increased by 140% in farmers’ fields using improved varieties and management practices. In addition to traditional organic and inorganic fertilizers, biochar and African Dark Earths have been found to improve soil properties and to enhance productivity, although their availability and affordability to African farmers remains to be explored. The concept of Integrated Soil Fertility Management (ISFM) has been successfully implemented in some African countries in the Great Lake Region. Other innovative technologies favorably accepted by farmers are the “Push-pull System” (an elegant method of controlling a devastating insect pest and a parasitic weed) and NERICA (New Rice for Africa, in which rice varieties with desirable nutritional and agronomic properties were developed by crossing Asian and African rice). This review calls for African governments and institutions not only to provide conducive environments but also to abide by the Maputo 2003 Declaration where they agreed to invest 10% of their national budget to agricultural research and development as the outcome has a positive impact on productivity and ultimately improves the livelihood of farmers.