Wheat is one of the most economically important crop species in the world. It provides twenty percent of calories to a global population of seven billion people. However, genetic research of wheat is complicated as the genome is very large, full of repetitive sequences and comprised of three similar sub-genomes. During the course of this project, the genetic resources available for wheat drastically improved. The abundance of genome-specific SNP markers increased considerably, and 2014 saw the release of a chromosome-based draft sequence of the hexaploid wheat genome. The wealth of publicly-available SNP genotype information was exploited, to identify statistical associations between SNP markers and agronomically important traits, using two experimental populations: the Avalon x Cadenza doubled haploid mapping population, and the NIAB elite Multi-parent Advanced Generation Intercross (MAGIC) population. Genomewide association, and QTL analyses identified regions of interest on chromosomes 3D, 4B 4D, 5A, 5B and 6A. These regions contained SNPs which had an association with either grain yield; grain weight; grain width; grain length; grain surface area; or a combination of these traits. Furthermore, regions of chromosomes IB, 2A, 5B, 5D and 6A were of particular interest as they not only contained SNPs with a statistical association with a trait, they contained a transcript that had differential expression between plants with high and low thousand grain weight. These results suggest that although genetic diversity is limited, there is still potential for the identification of yield-increasing genes within elite wheat. Due to the lack of sequence information for wheat, few of the sequences of interest were annotated with gene or protein function. However, a set of putative candidate genes have been identified in both populations, which appear to be involved in plant growth and development. Of particular interest to the wheat breeding industry is the range of elite material studied. Over 80% of allelic diversity seen in elite UK wheat was captured by the two experimental populations, which, in total, represented 10 elite varieties. Therefore, there is a high chance that the SNPs identified in these populations are segregating in elite breeding material. Furthermore, a variety of hexaploid, tetraploid and diploid wheat material, including elite varieties; wheat relatives; and wild landraces have previously been screened with the majority of the SNPs used in this analysis. The SNP data is publicly available, making the results of this study immediately available for validation or introduction into breeding programmes.