A caterpillar was the larval form of a butterfly. The change from caterpillar into butterfly was called metamorphosis. (TV: The Green Death)
The Eumenes was a genus of wasp which paralysed caterpillars and laid their eggs in their bodies, providing their larvae with an immediate food supply. (TV: The Ark in Space)
In the 1970s, caterpillars grew to giant size due to exposure to an improperly mixed insecticide spray. They were returned to their normal size by the Third Doctor. (COMIC: Insect)
On Telos, Jamie McCrimmon mistook a Cybermat for a caterpillar. (TV: The Tomb of the Cybermen) In the mid-20th century, the Cybermen of Mondas used caterpillar-like creatures which Ace identified as drones. (COMIC: The Good Soldier)
The Caterpillar Men resembled caterpillars, (COMIC: The Caterpillar Men) as did the Praxilions. (PROSE: Harvest of Time)
Kate Lethbridge-Stewart had a chrysalis theory regarding Susan Triad, that just because she was nice didn't mean that she couldn't change, that a caterpillar doesn't know that it's a butterfly and a phoenix is just a bird until it burns. (TV: The Legend of Ruby Sunday)