What is the best male and female athletics performance in history? We seek to answer this question for Olympic distance track events by simultaneously modelling race performances over all Olympic distances and all times. Our model uses techniques from a branch of statistics called extreme value theory, and incorporates information on improvements over time using an exponential trend in addition to a process which identifies the changing ability of the population of athletes across all distances. We conclude that the best male performance of all time is the 1968 world record of Lee Evans in the 400 m, and that the best female performance of all time is the current 1988 world record of Florence Griffith-Joyner in the 100 m. More generally, our approach provides a basis for deriving a ranking of track athletes over any distance and at any point over the last 100 years.