Plant breeders rely on heritable genetic variation for trait improvement, and the two primary novel sources of this variation are recombination and mutation of genetic material during meiosis. These independent processes can have overlapping significance for breeders, as the genetic resolution generated by recombination influences our ability to locate mutations. In addition, population improvement often results in inbreeding, which reduces the effective recombination and increases the likelihood of deleterious mutation hitchhiking via repulsion linkages. This is especially true in regions of chromosomes with low recombination rates, like the pericentromere. Polypoid crops pose an additional challenge to pinpointing the genetic control of desirable traits, as the phenotypic consequence of a single-variable locus (e.g., genomic structural variation) can be masked by the redundant copies of other homoeologous genomes. Here I address how geneticists can improve the accuracy of identifying targets for positional cloning, and whether breeders should seek to manipulate recombination to further harness the power of selection, using hexaploid wheat (Triticum aestivum L.) as a model. First, I present a study with a traditional approach to positionally clone a quantitative trait locus for yield components on wheat chromosome arm 5A. Leveraging a fine-mapping population, genomic data, phenotypic associations, early grain development transcriptome profiles, and predicted gene function, it was determined the quantitative trait locus was a result of strong linkage disequilibrium with a large deletion on wheat chromosome arm 5AS. This study highlights the phenotypic resiliency of polyploids harboring structural variants and actionable recommendations to increase the likelihood of identifying causal variants in wheat. Second, I used simulation models with empirical data to assess the potential of controlled recombination for genomic selection breeding programs. While controlled recombination remains under research and development, initial reports have prompted interest in evaluating increased recombination in the pericentromere to disrupt repulsion linkages. Comparing high and low values for a range of simulation parameters identified that few combinations under increased recombination retained greater genetic variation and fewer still achieved higher genetic gain. More recombination was associated with loss of genomic prediction accuracy, which often outweighed the benefits of disrupting repulsion linkages. Irrespective of recombination frequency and distribution and QTL location, enhanced response to selection under increased recombination largely depended on quantitative trait architecture, high heritability, more repulsion than coupling linkages, and greater than six cycles of genomic selection. Altogether, the results discourage a controlled recombination approach to genomic selection in wheat as a more efficient path to retaining genetic variation and increasing genetic gains compared to existing breeding methods.