Flameouts occur most frequently when the engine is at an intermediate or low power setting (such as during the cruise and descent phases of flight). Most of the time, they are recovered from uneventfully.
To recover from a flameout, the pilot should ensure the engine's fuel supply has been restored and then simply perform an engine restart as detailed in the aircraft's Flight Operations Manual.
Early jet engines, such as Junkers Jumo 004 used in early German jets, such as the Messerschmitt Me 262, were at relatively high risk of flameout. Fast acceleration or inappropriate throttle settings could impoverish the fuel/air mixture causing a flameout. If this happened at low altitude it would often lead to the total loss of the aircraft.
However, modern jets are engineered to a higher degree of technical quality and are controlled by systems (FADEC) that constantly fine-tune their performance; as such flameouts are not such a risk as they were in the early days of jet-powered aviation.
In 1982, British Airways Flight 9 suffered flameouts in all four of its engines after flying through a cloud of pyroclastic material thrown up by the eruption of Mount Galunggung. The pilots were eventually able to restart three of the engines and make a safe landing.
In 2004, Pinnacle Airlines Flight 3701 suffered flameouts in both of its two engines after flying too slowly at its maximum altitude. The pilots were unable to restart the engines, and the CRJ crashed near Jefferson City, Missouri.
In the film Top Gun, a flameout and flat spin is the cause for the crash of Tom Cruise's character's aircraft during a mock dogfight. The engine flameouts in the movie were simulated by turning off the stunt aircraft's afterburners.
Also, in the film Air Force One, a series of flameouts occur: before the evacuation, engine 1 is the first to flame out; as a badly injured man is seen leaving the plane, engine number 3 appears to have gone down; and as the president is shown on board the plane, number 2 engine flames out (the last to go).