Horse racing is a popular sport in many countries for racing on the flat, over obstacles, and with carts, because of the associated gambling. The wide range of bets available have attracted wide academic interest in predicting the outcomes, testing for efficiency of the betting markets, constructing betting systems, and predicting the turnover. This article discusses the key modeling issues raised in these different contexts, including the arguments about how to account for decreasing incentives down the finishing order and whether the inefficencies found are caused by risk preference or biased expectations.