I first got intrigued by iguanas when I watched a documentary about the marine iguanas of the Galápagos. These dive to feed on algae or seaweed growing on reefs but the other iguanas are land feeders although apparently they don't mind a swim. They vary widely in appearance and size and live in a range of habitats including tropical forest, desert and along rocky coastlines. Most are strictly herbivorous although according to livescience.com some enjoy worms, crickets and baby mice - I'm guessing the mouse eaters would be those kept as pets.
The green iguana, (Iguana iguana) has the greatest length of any iguana - it can reach two meters in length - and is a popular pet which can live for 15-20 years in captivity. I'm somewhat conflicted about this because, while I'm happy to keep as pets animals which are domesticated, I feel other animals really belong in their natural habitat. At the same time, I have to acknowledge that, because less than benign human activity has driven many creatures to extinction or its brink in the wild, if it wasn't for captive animals and the breeding programs associated with many of them (whether they are pets or in zoos), we would have to face the loss of some complete species. Tricky, isn't it. Happily, though, the green iguana is in not danger of extinction as it is one of the more common of its species and, as long as it is appropriately cared for, is no doubt content.
There's a lot of interesting information about the various kinds of iguana at this San Diego Zoo link.