Scientific strategies for crop improvement ensue from genetic knowledge gain from the relevant breeding populations. Few genetic studies were undertaken in Musa before the 1990s, despite the importance of the crop in human diet in the tropics. It was believed that genetic studies of most cultivated Musa, a virtually sterile triploid crop, were impossible. This explains the absence, until recently, of inheritance studies in triploid plantain and banana and the lack of genetic markers. Although several characteristics of the Musa crop make genetic analysis difficult, the production of euploid test-cross segregating populations obtained from triploid-diploid crosses has made inheritance studies possible. Thus, plantain and banana genomes have been investigated at the International Institute of Tropical Agriculture (IITA) since 1992. This paper provides insight into the genetics of black sigatoka and banana weevil resistance, pseudostem waxiness, virus susceptibility, apical dominance and suckering behavior, dwarfism, bunch orientation, fruit parthenocarpy, and male fertility. It also discusses the effects of genetic markers, ploidy and the environment on quantitative variation of disease and pest resistance as well as growth parameters of yield. This new knowledge has provided important information to develop IITA's scientific breeding strategy for the genetic improvement of plantain and banana.