Leiocephalidae, also known as the curlytail lizards or curly-tailed lizards, is a family of iguanian lizards restricted to the West Indies. One of the defining features of these lizards is that their tail often curls over. They were previously regarded as members of the subfamily Leiocephalinae within the family Tropiduridae. There are presently 30 known species, all in the genus Leiocephalus.

Iguania is an infraorder of squamate reptiles that includes iguanas, chameleons, agamids, and New World lizards like anoles and phrynosomatids. Using morphological features as a guide to evolutionary relationships, the Iguania are believed to form the sister group to the remainder of the Squamata, which comprise nearly 11,000 named species, roughly 2000 of which are iguanians. However, molecular information has placed Iguania well within the Squamata as sister taxa to the Anguimorpha and closely related to snakes. The order has been under debate and revisions after being classified by Charles Lewis Camp in 1923 due to difficulties finding adequate synapomorphic morphological characteristics. Most iguanians are arboreal but there are several terrestrial groups. They usually have primitive fleshy, non-prehensile tongues, although the tongue is highly modified in chameleons. Today they are scattered occurring in Madagascar, the Fiji and Friendly Islands and Western Hemisphere.