I explore the genetic and environmental basis of inheritance using modern techniques, in particular high-density genotyping arrays, and older techniques, in particular family history, to explore some longstanding questions about the way we inherit complex traits. Using pedigree data and the parent-offspring regression technique, I estimate narrow sense heritability (h2) of human lifespan in 20th Century Scotland as 0.16, lower than commonly cited studies in other populations. I also observe similar concordance between spouses as between parents and offspring - suggesting my estimate of heritability may include significant within-family environment effects and thus should be considered an upper bound. Using genome-wide array data to identify runs of homozygosity, from 150 cohorts across the world and up to 350,000 subjects per trait, I show that cognitive function and body size are associated with the total length of genome-wide runs of homozygosity. Contrary to earlier reports in substantially smaller samples, no evidence was seen of an influence of homozygosity on blood pressure and low-density lipoprotein (LDL) cholesterol, or ten other cardio-metabolic traits. An association between genome-wide homozygosity and complex traits arises due to directional dominance. Since directional dominance is predicted for traits under directional evolutionary selection, this study provides evidence that increased stature and cognitive function have been positively selected in human evolution, whereas many important risk factors for late-onset complex diseases have not. The analysis of less common single nucleotide polymorphism (SNP) variants in genome-wide association studies promises to elucidate complex trait genetics but is hampered by low power to reliably detect association, whilst avoiding false positives. I show that addition of 100 population-specific exome sequences to 1,000 genomes global reference data allows more accurate imputation, particularly of less common SNPs (minor allele frequency 1–10%). The imputation improvement corresponds to an increase in effective sample size of 28–38%, for SNPs with a minor allele frequency in the range 1–3%. Inheritance of complex traits remains a field wide open for discovery, both in determining the balance between nature and nurture and discovery of the specific mechanisms by which DNA causes variation in these traits, with the prospect of such discoveries illuminating biological pathways involved and, as knowledge deepens, facilitating prediction.