Determination of genetic variability, parameter estimates and improvement using traditional breeding technique alone is challenging. High degree of genetic heterozygosity, poor-flowering low seed set, variation in flowering intensity over seasons and across locations, low multiplication ratio of planting materials, genealogy overlap, polyploidy, biotic and abiotic stresses limit the efficiency of breeding progress in yams. The extent of genetic variability and selection gain in the crop is limited by lack of well-articulated information on genetic parameter estimates of quantitative traits. Knowledge of genetic parameter estimates and improvement of yam for tuber yield, quality and related attributes would facilitate the formulation of effective strategies for genetic conservation, management and utilization. Complementation of traditional method of computing genetic parameter estimates with molecular marker information is among the available handy tools for crop breeders to maximize genetic gain in a breeding program. This paper reviews the genetic variability and heritability in yam breeding, genetic improvement of yam for tuber yield and quality traits and related attributes. It assesses the limitations of genetic parameter estimates and the ways of improving genetic gain in yam breeding programs. Utilization of complementary techniques for determination of genetic parameter estimates in yam improvement programs can increase the selection gain and reliable exploitation of the heritable variation in the desired direction.