The horizon problem
Radio waves travel in straight lines. A ground radar 30 metres tall can see an aircraft flying at the same height only out to about 40 km — beyond that the Earth's curvature blocks the line of sight. The same radar on an aircraft at 10 km altitude can see for about 400 km. Putting the antenna up high is the cheapest way to extend coverage by an order of magnitude.
How AWACS works
The classic E-3 Sentry mounts a 9-metre rotating radome on top of a Boeing 707. Inside is an APY-1/2 pulse-Doppler radar that can spot fighter-sized targets at 400 km and track 600 simultaneously. Twenty operators downstairs run the air battle. Data goes by datalink to friendly fighters who don't even need to turn on their own radars — they fire missiles cued by the AWACS and stay invisible.
Why it's the single most important air asset
In the 1991 Gulf War, USAF E-3s coordinated 38 of the 39 air-to-air kills. The Iraqi Air Force never got within 100 km of a target. Modern AWACS — E-3, E-7 Wedgetail, A-50 Mainstay, KJ-2000 — are why air superiority is now mostly about who has better AWACS, not who has better fighters.
The replacement — distributed sensing
A single AWACS is also a single point of failure. Modern doctrine is shifting toward distributed sensing: dozens of stealth drones, each with a small AESA, datalinked into a synthetic AWACS. The aircraft you can see in 2030 air-power demos rarely includes a giant 707 with a frisbee on top.