The Red Queen's race is an incident that appears in Lewis Carroll's Through the Looking-Glass and involves the Red Queen, a representation of a Queen in chess, and Alice constantly running but remaining in the same spot.
"Well, in our country," said Alice, still panting a little, "you'd generally get to somewhere else — if you run very fast for a long time, as we've been doing."
"A slow sort of country!" said the Queen. "Now, here, you see, it takes all the running you can do, to keep in the same place. If you want to get somewhere else, you must run at least twice as fast as that!" 
The Red Queen's race is often used to illustrate similar situations:
- Isaac Asimov used it in his short story "The Red Queen's Race" to illustrate the concept of predestination paradox.
- Vernor Vinge uses it in his novel Rainbows End to illustrate the struggle between encouraging technological advancement and protecting the world from new weapons technologies.
- As an illustration of the relativistic effect that nothing can ever reach the speed of light, or the invariant speed.
- In evolutionary biology, to illustrate that sexual reproduction and the resulting genetic recombination may be just enough to allow individuals of a certain species to adapt to changes in the ecological niche they occupy - see Red Queen's Hypothesis.