In classical statistical genetic theory, a dominance effect is defined as the deviation from a purely additive genetic effect for a biallelic variant. Dominance effects are well documented in model organisms. However, evidence in humans is limited to a handful of traits, particularly those with strong single locus effects such as hair color. We carried out the largest systematic evaluation of dominance effects on phenotypic variance in the UK Biobank. We curated and tested over 1,000 phenotypes for dominance effects through GWAS scans, identifying 175 loci at genome-wide significance correcting for multiple testing (P < 4.7 × 10-11). Power to detect non-additive loci is much lower than power to detect additive effects for complex traits: based on the relative effect sizes at genome-wide significant additive loci, we estimate a factor of 20-30 increase in sample size will be necessary to capture clear evidence of dominance similar to those currently observed for additive effects. However, these localised dominance hits do not extend to a significant aggregate contribution to phenotypic variance genome-wide. By deriving a version of LD-score regression to detect dominance effects tagged by common variation genome-wide (minor allele frequency > 0.05), we found no strong evidence of a contribution to phenotypic variance when accounting for multiple testing. Across the 267 continuous and 793 binary traits the median contribution was 5.73 × 10-4, with unbiased point estimates ranging from -0.261 to 0.131. Finally, we introduce dominance fine-mapping to explore whether the more rapid decay of dominance LD can be leveraged to find causal variants. These results provide the most comprehensive assessment of dominance trait variation in humans to date.