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Laelaps was a Greek mythological dog who never failed to catch what he was hunting. He was a gift from Zeus to Europa. The hound was passed down to King Minos. Minos had been cursed by his wife; he ejaculated scorpions and spiders that would devour the genitals of those he slept with. Because of this, he called Procris of Athens to his aid. When she cured him he gave her Laelaps and a javelin that never missed its target. Procris's husband decided to use the hound to hunt the Teumessian fox, a fox that could never be caught. This was a paradox, a dog who always caught his prey and a fox that could never be caught. The chase went on for quite a while until Zeus turned both to stone, perplexed by their contradictory fates.

The name Laelaps was also given a genus of theropod dinosaur discovered in the marl pits of New Jersey (Navesink Formation, early Maastrichtian). Described by American paleontologist Edward Drinker Cope in 1866, after the mythological dog, the binomen Laelaps aquilunguis was changed to Dryptosaurus aquilunguis eleven years later by Cope's rival, Othniel Charles Marsh, when he learned that the name Laelaps had already been used (see below).

Laelaps is a genus of mites which are ectoparasites of rodents. The most familiar species is the spiny rat mite Laelaps echidninus due to the fact that it is a common parasite of fancy rats.