I have only really looked at the Allies' systems. War Emergency Power was a feature on some aircraft. Basically, by accessing the system (pushing a button, flipping a lever, or simply pushing a throttle past a wire "stop") could give a pilot access to increased power. Pushing the throttle past where it normally would stop is roughly equivalent to revving your car engine to or past the "red line". By getting more engine RPM's, you generally get more power, which can be critical in a dogfight. Other systems relied on water injection or methanol injection. Injecting water into the cylinder or the fuel-air mixture cooled the system down due to water's high specific heat (or to use the modern term, heat capacity). Cooler air resulted in a denser mist, with more combustion capacity. Methanol injection worked in a similar manner, while it cooled the engine it also reduced the ability of the fuel to detonate. This sounds counter-productive, but what it allowed was an increase in boost pressure from superchargers or turbochargers. So, you cranked up the boost pressure at the same time you injected a methanol mixture, giving you more power. There were also systems where increased boost pressure was available in some planes.

Each of these methods put a good deal of stress on the engine. Generally pilots were required to log the amount of time (usually minutes) of WEP used. After a certain amount, the engine would have to be inspected, disassembled, or even replaced. Using WEP was a calculated risk, but in an intense dogfight it could mean the difference between life and death. After all, the cost of a new engine paled with the cost of a pilot's lost life.