Although propeller engines have dominated the early 20th century, they have become obsolete in both military and commercial aircraft.  The successor of the propeller engine is the jet engine.  Jet engines are more powerful and at high speeds they become more efficient because of their aerodynamic form.  Similar to rocket engines, jet engines operate by thrusting air out of the rear of the engine which propels the aircraft forward.  Newton's third law states that forces act in equal action/reaction pairs, so the air that is pushed out of the rear pushes the engine forward.  The most commonly used engine today is the turbofan engine.  F-15 Eagles are one example of a modern day fighter that utilizes the turbofan engine.

    A turbofan engine operates first by compressing the incoming air through a series of compressor fans into the combustion chamber.  Inside the combustion chamber, the air is sprayed and mixed with fuel.  The mixture of gasses is then ignited and the reaction of hot gasses is ejected out of the rear.  Before the gas reaches the nozzle, some of its kinetic energy is directed towards turning a turbine which turns the compressor fans, allowing fresh intake of air into the combustion chamber.  The turbine also turns the outer fan which not only distributes air into the combustion chamber, but also redirects air around it, generating extra thrust like a propeller engine.
    Most fighter jets also have afterburners next to the nozzle.  The afterburner generates additional thrust by igniting additional fuel near the nozzle, allowing the jet to reach supersonic speeds.