The Federal Aviation Administration (FAA) has a duty, among others, to ensure that use of the National Air-space System (NAS) is distributed equitably (fairly) amongst all claimants. In particular, the FAA must ensure that landing rights are fairly distributed. Ordinarily, this is not a problem, as most airports can usually accommodate all arrival demand. Occasionally, exigent circumstances (usually adverse weather conditions) require that an airport reduce aircraft arrivals to some rate below the level of demand. The issue then arises of which flights should be allowed to land when. In the interests of safety and fuel-economy, the FAA attempts to delay flights on the ground, before they depart, rather than in the air. Each flight is assigned a time slot when it is to arrive, and takes off just in time to meet its arrival slot. People have debated the problem of fairly dividing limited assets for several millennia. Recently (since about 1950) mathematicians and economists have proposed various axiomatic notions of fairness. I will discuss several formal and informal notions of fairness, and examine their implications for allocating arrival slots.