The quantitative geneticist W. G. ('Bill') Hill, awardee of the 2018 Darwin Medal of the Royal Society and the 2019 Mendel Medal of the Genetics Society (United Kingdom), died on 17 December 2021 at the age of 81 years. Here, we pay tribute to his multiple key scientific contributions, which span population and evolutionary genetics, animal and plant breeding and human genetics. We discuss his theoretical research on the role of linkage disequilibrium (LD) and mutational variance in the response to selection, the origin of the widely used LD metric r² in genomic association studies, the genetic architecture of complex traits, the quantification of the variation in realized relationships given a pedigree relationship and much more. We demonstrate that basic theoretical research in quantitative and statistical genetics has led to profound insights into the genetics and evolution of complex traits and made predictions that were subsequently empirically validated, often decades later.