In sub-Saharan Africa, sweetpotato weevils are the major pests of cultivated sweetpotato, causing estimated losses of between 60% and 100%, primarily during dry spells. The predominantly cryptic feeding behavior of Cylas spp. within their roots makes their control difficult, thus, host plant resistance is one of the most promising lines of protection against these pests. However, limited progress has been made in cultivar breeding for weevil resistance, partly due to the complex hexaploid genome of sweetpotato, which complicates conventional breeding, in addition to the limited number of genotypes with significant levels of resistance for use as sources of resistance. Pollen sterility, cross incompatibility, and poor seed set and germination in sweetpotato are also common challenges in improving weevil resistance. The accurate phenotyping of sweetpotato weevil resistance to enhance the efficiency of selection has been equally difficult. Genomics-assisted breeding, though in its infancy stages in sweetpotato, has a potential application in overcoming some of these barriers. However, it will require the development of more genomic infrastructure, particularly single-nucleotide polymorphism markers (SNPs) and robust next-generation sequencing platforms, together with relevant statistical procedures for analyses. With the recent advances in genomics, we anticipate that genomic breeding for sweetpotato weevil resistance will be expedited in the coming years. This review sheds light on Uganda's efforts, to date, to breed against the Cylas puncticollis (Boheman) and Cylas brunneus (Fabricius) species of African sweetpotato weevil.