The Holy Grail of the aerospace industry is the supersonic combustion ramjet (scramjet).
The scramjet differs from the ramjet in that combustion takes place at supersonic air velocities through the engine. It is mechanically simple, but vastly more complex aerodynamically than a jet engine. Hydrogen is normally the fuel used. The only one that has been operated outside a wind tunnel (and then limited) was flown on the end of a Russian rocket. The testers think they got positive thrust.

A scramjet has to be moving at about Mach 5 or so just to get started. Supposedly a scramjet can operate up to about Mach 12. Anyway, here's my idea of how a scramjet could be made to operate.

The first of these is a 3D scramjet with an annular inlet and combustion chamber. Part of the air is ducted into the center-body where it is combined with an excess of of fuel (possibly a hydrocarbon). This fuel is heated by partial combustion with the air and then exhausted alongside the supersonic airflow of the main engine. This hot fuel mixes with the air, autoignites, and exhausts out the back to provide thrust. The advantage is that hydrocarbons can be used, as opposed to hydrogen, some of the complex step-type flame holders are eliminated, and it can provide more thrust at lower speeds. Some scramjet designs try to perform the same function with rocket engines.

The second image is of a 2D scramjet as it would be mounted under the fuselage of an aircraft. Again, the airflow is split between the ramjet and the scramjet.