The Lockheed Martin TR3B is (or is thought to be) an aircraft which uses anti-gravity propulsion. There are few questions about it that are answered, its existence is not fully acknowledged, albeit the US Air Force almost certainly has several TR3Bs.

It seems that the majority of respected physicists and people of associated peripheral skills are disdainful of the possibility of anti-gravity principles being able to be successfully implemented to any useful degree. There are some interesting very small scale and very brief examples that supposedly prove the viability of anti-gravity but credible physicists and people of associated peripheral skills have to date not been able to replicate these examples.

What is your belief about anti-gravity? There are crackpots who believe that anti-gravity has been successfully deployed in secret aircraft after being reverse engineered from crashed alien craft.