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Long before the publication of Darwin's theory of evolution by natural selection and Mendel's work on genes, horses were being selectively bred for improved racing performance. This resulted in the creation of a highly specialised breed of racing horse, known as the thoroughbred. Throughout the 19th century the winning times of the most elite thoroughbred races in Great Britain declined, suggesting genetic evolution of faster speed was ongoing in response to selective breeding. However, several studies have reported a slowing of the rate of improvement since early in the 20th century, leading to a consensus amongst scientists and industry experts that thoroughbred speed has reached a selection limit. The broad aims of my PhD thesis are to understand the genetic basis of variation in racehorse speed, and in doing so, to determine if thoroughbreds have indeed reached a genetic limit for how fast they can run. If so, what is constraining further improvement? Moreover, can a better understanding of the factors that determine the rate of improvement in thoroughbred speed allow us to design breeding programmes that would overcome this supposed limit? To do this, I apply quantitative genetic tools, developed for improving livestock since the mid-19th century but largely passed over by thoroughbred breeders, to a vast pedigreed dataset of thoroughbred performances in Great Britain. Firstly, addressing limitations of previous studies, I set out to characterise more accurately the current and historical rate of phenotypic improvement in thoroughbred speed. Secondly, I apply quantitative genetic analysis to determine the extent of heritable variation for this trait and assess whether phenotypic rates of improvement in speed - if still ongoing - are underpinned by a genetic response to selection. Next, I investigate the possibility that maternal and/or paternal age at conception may affect offspring racehorse speed and examine whether parental identity is an important source of variation in offspring performance. If so, is there any genetic basis of maternal or paternal variation identified, and what are the implications for selection response? Finally, in an essay I explore the history of equine (and jockey) welfare concerns in the sport, and consider the role quantitative genetics could play in reducing equine injury susceptibility alongside improving performance. Lastly, I discuss my findings and consider future directions for this research.