Events like the World Championships in athletics and the Olympic Games raise the public profile of competitive sports. They may also leave us wondering what sets the competitors in these events apart from those of us who simply watch. Here we attempt to link neural and cognitive processes that have been found to be important for elite performance with computational and physiological theories inspired by much simpler laboratory tasks. In this way we hope to inspire neuroscientists to consider how their basic research might help to explain sporting skill at the highest levels of performance.