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Common solutions for aerobatic piston singles is to have either header tanks (for wing tanks, as I understand it) or flop tubes (for fuselage tanks).
Do fuel systems in a fighter jet work on the same principles? Or are they somehow smarter to allow more erratic maneuvers?

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I don't know for certain as I'm not military, but I imagine that they pressurize the fuel tanks using bleed air, much like jet airliners do. It's also likely that they make use of boost and ejector pumps to provide positive pressure directly to more centrally-located tanks which the engines then feed from.

enter image description here (from FAA AMT Handbook [pdf])

The F-15 has both wing & fuselage tanks; according to a site of dubious accuracy (F-15E.info):

The left and right engine feed tanks contain baffles in order to provide a limited amount of fuel to the boost pumps during inverted flight or during negative G maneuvers

enter image description here

  1. Left wing tank
  2. Auxiliary tank
  3. Left engine feed tank
  4. Right wing tank
  5. Right engine feed tank
  6. Tank 1 (main tank)

Baffles are dividers in the tank itself that limit the speed at which fuel can flow from one end to another, usually to prevent fuel sloshing and screwing up balance.

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  • $\begingroup$ Pressurizing the tanks to push the fuel in makes sense. I see how baffles would prevent sloshing, but how can they prevent the boost bumps from sucking in air during a negative G maneuver or inverted flight (being technically the same as -1 G)? $\endgroup$ – falstro Jan 21 '14 at 7:53
  • $\begingroup$ @roe I think it's basically that they prevent the fuel from immediately sloshing to the bottom of the tank (sloshing can include top to bottom, right?). $\endgroup$ – egid Jan 21 '14 at 19:57
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    $\begingroup$ From what I've heard by asking around, the baffles compartmentalize the fuel tank, and restricts the flow between each compartment. Basically, it works like when turning a water bottle upside down, unless there's a hole in the bottom (now top) of the bottle, air is going to have to flow in as water flows out. The compartments are basically a bunch of chained bottles, air would have to flow into the first one, before being able to reach the second and so on. There is a whole on the other side, but it's one way (the pump), so fuel flows a lot better in that direction. $\endgroup$ – falstro Feb 7 '14 at 14:30
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    $\begingroup$ The engine feed tanks (2-3 & 5) are kept full at all times by the pumps in all the other tanks. The baffles in the engine feed tanks are needed to keep fuel in the bottom of the tanks while the aircraft is upside down, because some genius decided that all the pumps should be at the bottom of the tanks. BTW, tank 1 (6) is not the main tank. The engine feed tanks are the main tanks. $\endgroup$ – user2225 Apr 27 '14 at 20:42
  • $\begingroup$ Some military jets do indeed have simple inverted pickups, but most modern ones have more advanced fuel systems $\endgroup$ – SSumner Sep 27 '14 at 23:57
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The F-16 operates in a similar way to egid's answer. There are 7 internal fuel tanks with the possibility of 3 external tanks.

On the left system:

Left internal tank
A-1
Aft reservoir

On the right system:

Right internal tank
F-1
F-2
Fwd Reservoir

Possible external tanks:

Left external tank (flows into left internal tank)
Right external tank (flows into right internal tank)
Centerline tank (flows between left and right system)

The external tanks flow into their respective internal tanks. The reservoir tanks are the engine feed tanks that flow through the engine feedline to the fuel flow proportioner and eventually to the engine.

Getting to your question... The primary way fuel is transferred through the system is by siphoning using air ejectors. However, this is only used in upright flight. In addition there are boost pumps in the fuel tanks. The #3 boost pump is actually near the top of one of the reservoir tanks and provides fuel during inverted flight. While inverted, fuel does not transfer from the external tanks to their respective internal tanks.

Even with this setup, the jet is restricted to only 30 seconds in MIL or less power and 10 seconds while in AB during negative G flight.

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