Heathrow, the largest of these airports, is full and others are increasingly constrained. There is a broad consensus on the need for new airport capacity.
A number of proposals have been put forward. Among these, the owners of Heathrow and Gatwick each proposed an additional runway.
The Mayor proposed three potential sites for locating a new four-runway hub, each to the east of London, away from heavily populated areas:
Find out more about the relative merits of these five expansion options in the 'Landing the right airport' report on the Aviation page in Publications & reports.
On that page you can also read the full range of Mayoral submissions as well as a number of accompanying detailed technical reports.
The Airports Commission was set up by the Government to consider this aviation capacity challenge.
The Commission presented its Final Report to Government in July 2015. It recommended a third runway at Heathrow Airport.
In December 2015, the Government chose not to accept the recommendation. Instead, it pledged to do more research on each shortlisted option to better understand their impacts on air quality, noise, carbon emissions and local communities.
The Airports Commission has now been disbanded.
A hub airport serves both people travelling to or from the catchment area of the airport and passengers changing planes at the airport. It should be able to allow for more routes, run more frequently, than a non-hub airport could.
Heathrow is an imperfect hub today because it is effectively full. This limits the number and frequency of routes it can offer. It also erodes the airport's resilience and leads to increased delays.
The Airports Commission's evidence shows that a third runway at Heathrow would be full shortly after opening. It predicts that just seven new daily long haul routes would be served by an expanded Heathrow - and three fewer domestic destinations.
By contrast, a new four-runway hub airport would have enough capacity to support 87% more daily long haul destinations, according to the analysis done. It would also double the number of UK cities served, giving them better access to other parts of the world, via the hub.
According to the Airports Commission, a three-runway Heathrow would expose more than half a million people to significant aircraft noise. That is more than the number of people exposed by its five main European rivals combined.
Analysis for TfL estimates that as many as a million people could be exposed, based on assumptions similar to today's operations.
Air quality is also a concern for Heathrow. Without expansion it is predicted that Heathrow will have the third worst air pollution in London. There is a risk that a third runway would mean the roads around Heathrow breaking the legal limits for air pollution.
A new airport to the east of London, away from populated areas, could address these public health issues. Modelling indicates a 95% reduction in the number of people exposed to significant aircraft noise by a hub at Stansted or the Inner Thames Estuary. Neither would have any notable impact on air quality.