Iguana communication is physical. Their words are formed by the arrangement of their body and body parts (posture), movements (stylized walking, strutting, bobbing), and use of three-dimensional space (where they're in vertical space, seeking height or flattening out).
Iguanas, then, have developed a limited (in human terms) vocabulary, one that — like some spoken languages — has some very subtle nuances in pronunciation. They're easily able to communicate with other iguanas in this language of the body. Although iguanas are able to learn some spoken words or sounds that we make (such as their names or the sound of the refrigerator door opening), they can effectively communicate to us only in the language they know best. It's up to us to learn to read their language — interpret their postures and movements — to understand what they're saying. Once you learn their language, you can also use some of their "words" to talk to them.
Posture
The usual iguana-at-rest-but-alert posture is rather like a dog. The body is flat on a surface with knees bent, feet back, and forearms flat, but the head and neck are raised. From this position, it's easy for them to go to sleep. Sometimes they doze with their head up but eyes closed, but usually the head goes down onto the surface they're lying on — or on their arms or resting on some object. When they're in deep-sleep mode, their fore- and hindlegs may be extended back along their sides ("the swimmer" position); some may even throw one of their legs up over their tail.
From the sphinxlike starting position, it's also easy for them to raise up into an alert crouch or into a full standing position. The crouch may be in response to something that mildly startles the iguana or to some serious petting by you, as the iguana arches its back to meet your hand.
When two iguanas, generally two males, are battling one another for dominance, the one giving up adopts the "surrender" posture. It almost looks like a dog soliciting play: The forelegs and hands are on the ground, elbows slightly flexed for rapid movement if necessary, the body is low to the ground, and the hindquarters are slightly raised. The head and neck are plastered to the ground. This is the subordinate iguana's way of signaling that he is lower than a worm and of no threat or competition to the dominant iguana. For now.
The dewlap
The dewlap is more than just a solar heater; it's part of the iguana's communication system. When it's tucked up tight or flared stiffly out, you can read the iguana like a book.
When the dewlap is tucked up under the chin, an adult or juvenile iguana is signaling submission or a state of nonaggression. A baby iguana who's trying to present as nonthreatening a profile as possible keeps his dewlap tucked up tight, too.
When dewlaps are relaxed, they flop down and sway when the iguana moves. In large iguanas, especially males, the dewlap is long, wide, and luxuriously silky, hanging in folds like a curtain.
When the dewlap is rigidly extended, its leading edge actually slants forward a bit. This flaring out is used both offensively and defensively. Offensively, it may be part of a threatening gesture, a warning that here is a big iguana not to be messed with. It typically occurs when something or someone new enters the iguana's environment. Being unsure what it is or what type of threat it may present, the iguana issues a preemptive warning first.
When the flared dewlap is combined with the tall stance, laterally compressed body, and erect nuchal and dorsal crest, the iguana is seriously working at intimidating someone or something. If the iguana is at a level higher up than the object of its intentions, it may also lean over to make sure that the object gets the full effect of the posture. Funnily enough, iguanas on the floor lean over, too, trying to intimidate the person or animal standing over them. If they're presenting this posture to you, and you lean over them, some keep leaning until they flop right over.
The swagger
The swagger is a male thing, carried out by an iguana threatening, or trying to court, a human or another iguana (or dog, cat, stuffed toy animal, and so on). In this stylized walk, the body is compressed laterally to make it look taller, and the lizard stands on straightened legs. As the lizard walks, the tail is slightly arched up behind the hind legs and may be swished from side to side. The dewlap is fully extended downward. When approached, such iguanas lean over away from you or circle around you, attempting at all times to present the biggest possible broadside profile to you to maintain their threatening or "come hither" look.
Tail twitching
The tail twitch may be part of the swagger, or it may be done when the iguana is at a standstill. The last half of the tail twitches, much like the tail of a cat that's stalking a bird or ball of yarn. This movement seems to signify a condition of mixed motivations — like when a male iguana wants to attack its female human keeper to mate with her but knows that such an action won't be received with the same spirit in which it was intended. In such a mixed-emotions state, the iguana may be hunched up, the body in compressed and broadside presentation, but with the head down, dewlap semirelaxed, similar to the submission/subordinate position, with the tail twitching slowly back and forth.
The eyes
Eyes wide open or eyes wide shut, iguanas are quite expressive with their deep brown to light hazel eyes. The one look that every iguana keeper becomes familiar with is the infamous "iguana glare" or "stink eye." Whether delivered straight on or thrown back over the shoulder, the glare is the primary way disgruntled iguanas put their annoying keepers in their proper place.
Iguanas also communicate with their eyes closed. When the eye closest to you is closed but the other eye is open, it's actually a sort of compliment. It means that the iguana is comfortable with you but is keeping an eye out on what's going on around him.
When you first get your iguana, chances are he'll spend a great deal of time in your presence with both eyes closed. This is his way of escaping from the overall stress of the situation, with the new home, people, noises, smells, routines, and strange new foods leading to sensory overload. He closes both eyes as a way to reduce the stimuli and shut everything out. As time goes on, and your iguana becomes acclimated to you and his new home and family, you'll find that the closing of both eyes happens rarely. Eventually, you'll see that it most often happens when you're engaged in a petting session — and the closed eyes and relaxed posture reflect iggy nirvana. You'll also find that it happens when they've insinuated themselves among your fragile bric-a-brac, and you have the nerve to start yelling at them as you move everything away to extricate them.