The foot is a pretty vital structure in cycling, especially if you are a competitive cycler. We depend on the foot to transfer all the load and forces to the pedal to work harder. The structure, integrity and comfort is vital to that process. Any problems are going to lessen performance if you are a competitive athlete and be a source of discomfort if you are a recreational cyclist.
Podiatrists diagnose and treat problems of the foot and often are very involved in cycling issues from the pain that can occur in the foot, to the set up of the bike, footwear and pedal and also the alignment issues of the foot for optimum performance and injury treatment and prevention. They will give advice on cycling footwear and the correct fit. Typically that footwear has to be quite tight fitting, which can result in a range of problems from pinched nerves and numb feet. Podiatry often use cycling orthotics to help these types of problems and to improve foot alignment. There was a good discussion on Podiatry Arena between podiatrists on foot othoses and cycling that is worth browsing if you want to follow this topic. In addition, they have these threads on cycling.
PodChatLive has this episode on Podiatry and cycling and this explain more about foot orthotics and what podiatrists can do to help the foot problems in cyclists.