This is a 737-200. It has two JT8D turbofan engines that live happily in pods underneath the wings, guzzling down air and Jet-A.
This is an ME-262. It has two Jumo 004 engines that live... not exactly happily in pods under the wings, guzzling down air and whatever the Nazis had that was flammable.
This is an F-14A of VF-84 "Jolly Rogers." It has two TF30 low bypass turbofans that sit at the end of long inlets with three variable-geometry shock ramps, a variable-position spill door and a boundary layer diverter per engine. These elements are computer-controlled to optimize pressure recovery, oblique shock wave location, minimize spillage drag and keep flow distortion to a minimum.
Air intake design in combat aircraft turns out to be extremely complicated.
Unlike an airliner, which is expected to cruise at subsonic speeds all the time, and unlike a wunderwaffe, which is expected to vaguely work enough so that the Americans give you a cushy technical consultant's job after the war instead of leaving you for the Russians, a modern fighter air intake has to work well at subsonic speeds, at supersonic speeds, when the fighter is maneuvering, it must deliver undistorted air to the engines, and it must be as light and offer as little drag and other aerodynamic disruptions as possible. Oh yeah, and nowadays it should contribute as little as possible to radar cross section. Have fun!
For good subsonic performance, the air intake has to produce smooth, gradual transitions in flow as it is decelerated and finally fed into the engine. This produces a decrease in dynamic pressure and a corresponding rise in static pressure. A relatively simple and light inlet design can do this well.
For supersonic flight, things get more complicated. The air must be decelerated to subsonic velocity by a shock wave, or, ideally, by a series of shocks. The exact position and angle of the shock waves changes with mach number, so for very best efficiency, the intake requires some sort of variable geometry.
The first supersonic fighters used nose-mounted intakes.
In a number of designs, there were central shock-producing spikes that also doubled as radar mounts:
In these designs the shock cone could translate forwards and backwards some amount to optimize shock location.
However, as radar became more and more important to air combat, shock-cone mounted radars ceased to be large enough to fit the wide, powerful radar sets that designers wanted. The air intakes were moved to the sides and bottom of the aircraft.
This Q-5 is a particularly good example because the design was originally based one that had a nose-mounted intake (the J-6/MiG-19).
Putting the intakes on the sides does get them out of the way, but it causes another problem. Airflow moving over the surface of the fuselage develops a turbulent boundary layer, and ingesting this turbulent boundary layer into the engines causes problems in the compressors. Aircraft with intakes mounted next to the fuselage, therefore, require some means of keeping the boundary layer air from getting into the engines. Usually this is accomplished by having a slight offset and a splitter plate:
However, there are other means of boundary layer management. The JSF and the new Chinese fighter designs use diverterless supersonic inlets:
In these a bump in front of the inlet deflects the boundary layer away from the engine intake using sorcery advanced fluid dynamics. This system is lighter, and probably allows better stealth than traditional inlet designs.
Fighters must be able to maneuver, sometimes violently, and this can affect airflow into the engines. Placing the air intakes underneath the fuselage, or underneath the wings helps the situation at high angles of attack, as the fuselage or wing helps deflect the airflow towards the intakes:
The intake location of the F-16:
and also the MiG-29:
Take advantage of this fact.
Finally, air intakes are potentially large sources of radar returns, so on modern designs they have to be tailored to minimize this problem. One of the biggest ways to do this is to hide the engine's compressor blades from the front, as large, whirling pieces of metal are very good radar reflectors:
As you can see, the compressor face of the engine in the YF-23 is almost completely hidden. You can also see that the inlet duct avoids right angles that would act as retroreflectors, and that it has an unusual boundary layer management system.
There is a lot more ground to cover, but these are the basics of how combat aircraft air intakes work, and why they look the way they look.