Aerodynamics has such a profound impact on cycling performance at the elite level that it has infiltrated almost every aspect of the sport from riding position and styles, equipment design and selection, race tactics and training regimes, governing rules and regulations to even the design of new velodromes. This paper presents a review of the aspects of aerodynamics that are critical to understanding flows around cyclists under racing conditions, and the methods used to evaluate and improve aerodynamic performance at the elite level. The fundamental flow physics of bluff body aerodynamics and the mechanisms by which the aerodynamic forces are imparted on cyclists are described. Both experimental and numerical techniques used to investigate cycling aerodynamic performance and the constraints on implementing aerodynamic saving measures at the elite level are also discussed. The review reveals that the nature of cycling flow fields are complex and multi-faceted as a result of the highly three-dimensional and variable geometry of the human form, the unsteady racing environment flow field, and the non-linear interactions that are inherent to all cycling flows. Current findings in this field have and will continue to evolve the sport of elite cycling while also posing a multitude of potentially fruitful areas of research for further gains in cycling performance.