Wheat grain yellow pigment content (GYPC) is an important trait that determines pasta quality. The main objective of this review is to examine the genetics regulating GYPC to enhance it through breeding, leading to improved pasta quality. Although GYPC is a polygenic trait, its high heritability has facilitated breeding internationally. GYPC is influenced by one or two major loci with additive effects plus several minor genes, and there is evidence showing that the phytoene synthase loci PSY1A and PSY1B are strong candidate genes that regulate GYPC. Nine Chilean durum wheat (Triticum turgidum L. var. durum) genotypes showed intermediate to low levels of GYPC based upon both phenotypic and genotypic data. The next step is to improve GYPC in those materials by introgressing the high-yellowness PSY1 allelic variants (i.e., the PSY1Ao allele and the PSY1Bb allele) using plant breeding strategies such as backcrossing and marker-assisted selection.