Quantitative traits and disease risk in humans are affected by both genetic and environmental factors. Using genome-wide association studies (GWAS) over the past decade, researchers have been successful in finding common genetic polymorphisms that explain a proportion of the variation in many common phenotypes. Despite these significant leaps forward in our understanding, the heritable components of many traits remain largely unaccounted for. A number of explanations as to the “missing heritability” of complex traits and disease risk have been postulated. This thesis addresses some of the unexplained potential sources of heritable trait variation and explores two of its potential causes: low frequency and structural genetic variation. Chapter 1 provides a background to GWAS, what we have learned from them, discusses the different mechanisms of heritability and reviews the potential explanations for “missing heritability” in complex traits. The chapter then describes low frequency and structural genetic variation and how they fit into the spectrum of genetic variation. Chapter 2 describes a study that tests the extent to which low frequency association signals can be discovered through low pass whole genome sequencing when using well-powered gene expression and biomarker phenotypes as model traits. The study then compares these association signals to 1000 Genomes based imputation in the same individuals. Chapter 3 uses methods to detect the structural forms of the human amylase locus with whole-genome sequencing data. The study detects and validates multi-allelic copy number within this region and finds a lack of evidence of a previous association between structural variation of the amylase locus and obesity and body mass index. Chapter 4 scans for rare copy-number variation (CNV) using SNP microarray data from over 120 thousand individuals at 69 sites that were previously identified as being associated with developmental delay. The chapter aims to refine their prevalence in the general population and attempts to understand their relationship with developmental delay and complex traits. Chapter 5 aims to detect large deletions and duplications genome-wide using SNP microarray data in a sample of over 120 thousand individuals where we have power to detect rare copy number events. I used novel approaches to test their association with 204 clinically relevant complex traits to determine their role in the heritability of complex traits. Chapter 6 discusses the findings from the previous chapters within this thesis. I then continue by describing some limitations of this work and explore the potential further directions for future work in this area of study.