This famous Tyrannosaurus Rex is named "Sue" and is on display at the Field Museum of Natural History in Chicago, Illinois.
The undisputed King of Dinosaurs
The undisputed most popular and well-known dinosaur on Earth has fascinated everyone everywhere since it was first described in 1905. Look at some of the language used by the New York Times in December of that year to describe Tyrannosaurus Rex:
"The most formidable fighting animal of which there is any record whatever."
"King of all kings in the domain of animal life."
"The absolute warlord of the earth."
"A royal man-eater of the jungle."
Okay, that last one is pretty funny, since humans came about tens of millions of years later. However, this sort of excitement and amazement that such an animal really existed has never decreased, and this ancient reptile remains absolutely fascinating.
Since the discovery of tyrannosaurs, other large carnivorous dinosaurs have also been discovered which might not be as well known to the general public, although they are certainly amazing and impressive every bit as much as the undisputed most popular and well-known dinosaur ever. Some may have outweighed Tyrannosaurus Rex, and were certainly longer, especially Spinosaurus.
Our understanding of dinosaurs and also of individual species has continued to evolve over time. When movies have portrayed dinosaurs in recent decades, certainly great effort was taken in many instances to portray them accurately. However, new discoveries inevitably lead to finding out we were wrong about some things.
What is shared below is what is currently known about Tyrannosaurus Rex, and I intend to update this information as new discoveries are made. Anyone who has a correction or any additional information is invited to leave a comment below or to contact me through my blog.
The Lost World (1925) and King Kong (right) were big hits and rightfully so. Each featured dinosaurs at the best they had ever been depicted on film. 
Tyrannosaurus Rex in the movies
Movies have as stated typically reflected what was known about dinosaurs at the time, although limitations also existed in the past due to special effects capabilities.
In the 1925 film The Lost World, an adaptation of a book by Arthur Conan Doyle, T-Rex was portrayed standing upright with its tail dragging on the ground, and it has three fingers on each hand. In one scene it fights with a Brachiosaurus. At the time this movie had amazing special effects, and it was rightfully a big hit. Interestingly, the carnivorous dinosaur in the book is Allosaurus but the movie makers wanted it to be T-Rex.
In the 1933 film King Kong, there is a climactic battle between King Kong (a giant ape if you didn’t know) and a T-Rex. The battle was difficult to create for the film and required special effects by the same guy (Willis O-Brien) who had done them for The Lost World eight years earlier. The appearance of T-Rex in King Kong was basically the same.
Disney’s 1940 animated film Fantasia showed T-Rex basically the same way yet again.
T-Rex didn’t start to have the correct posture until a few decades later. One of the first appearances of T-Rex in which posture and anatomy were correct was a short 10-minute film called Prehistoric Beast (see it below). The success of this shorter film led to a full-length television documentary about dinosaurs in 1985, called Dinosaur! By today’s standards the effects don’t seem all that great, but at the time these came out they were quite good. In fact, Dinosaur! Won the Primetime Emmy Award for Outstanding Visual Effects in 1986.
A new and much higher standard was set by the release of Jurassic Park in 1993. Unprecedented effects gave the dinosaurs a realism never before seen. Like many kids at the time, the movie instantly became my favorite. In Jurassic Park the T-Rex is fast moving and has a terrifying otherworldly roar. It also returns as a main character in the second movie in 1997, and has a much smaller role in the third movie in 2001.
Tyrannosaurus Rex also returned for the fourth JP movie, released in June 2015, and the dinosaur's appearance was the same as before for continuity, even though it’s now known that there are some significant inaccuracies.
There are of course a number of other movies which depict T-Rex, although the ones mentioned above stand out to me as being the most important to mention here.
1984 short film: Prehistoric Beast
This film led to the documentary film Dinosaur! a year later, and is one of the first to depict T-Rex with the correct posture. 
Tyrannosaurus Rex in real life
You may be wondering: If Jurassic Park is the most accurate so far, what about it is inaccurate? Many dinosaur fans are now aware that T-Rex probably had at least some feathers, and possibly lots of them. This wasn't known when the first three films were made.
In 2012 an Asian tyrannosaur species was discovered called Yutyrannus. Amazingly, the fossils were very heavily feathered. Prior to this, in 2004 another tyrannosaur species called Dilong had been known to have some feathers, although those of Yutyrannus were far more.
Feathers don't preserve well as fossils from tens or hundreds of millions of years ago, and so although no fossils for T-Rex have been found with feathers, the fact that relatives had them has led many paleontologists to conclude that T-Rex very likely had them as well. Amount and coloration are unknown.
There’s another problem with the T-Rex in Jurassic Park (and T-Rexes shown in many other films), and it is the fact that they probably could not roar. In order to roar it would need special soft tissue structures in the throat, basically a voice box like a lion has. Currently there is no evidence that this existed in any dinosaurs, although it isn’t entirely impossible. Such a thing being preserved in fossils would be incredibly rare if it had ever evolved in any of the dinosaurs, so it’s likely that if dinosaurs had the capability of roaring we would probably not be able to find out about it through fossils. But it's unlikely this was the case.
Dinosaurs are related to birds, or you could say that birds are the only dinosaurs that are still alive, although they have evolved much since all other types of dinosaurs went totally extinct 65.5 million years ago. Therefore one possibility for what T-Rex sounded like comes from large flightless bird species such as emus and cassowaries, which make low booming calls.
Another possibility is that T-Rex and other dinosaurs made croaking sounds similar to crocodiles. Roaring however is very unlikely.
So what I'm waiting for is a movie showing a T-Rex with feathers and no ability to roar! Science fanatic that I am, I'd love to see that, even though adding feathers to a computer-generated dinosaur would be much more difficult than a bald and featherless dinosaur. I have faith however that it will happen.
Calls of the cassowary
This large flightless bird species is native to Australia and New Guinea.  The sounds they make give us clues for what dinosaurs may have sounded like. 
More basic facts about Tyrannosaurus Rex
T-Rex was one of the last dinosaur species (not counting birds) to live upon the Earth, in the last 2 million or so years of its existence up until a massive asteroid or comet hit the Earth 65.5 million years ago.
T-Rex is known to have reached 40 feet (12 meters) in length, and probably weighed between 12,000 and 15,000 lbs (5,400 and 6,800 kg). The magnificent specimen called Sue, shown in the first photo above, is 40 feet (12 meters) in length.
The bite force of T-Rex was more powerful than any land animal ever known, including other large carnivorous dinosaurs. There are many estimates, although the average seems to be between 8,000 and 12,000 psi (pounds per square inch). It certainly would have been able to crush bone.
T-Rex lived in the western half of North America, which at the time was separated from the eastern half of the continent by a seaway. Other tyrannosaur species lived in North America and Asia during the Cretaceous Period (145 to 65 million years ago).
T-Rex is known to have hunted at least some of the time. The debate about whether it ever hunted or just scavenged seems to have been settled by a tooth embedded in the tail of a Hadrosaurus, an herbivore that T-Rex enjoyed the taste of. This is good evidence that T-Rex hunted Hadrosaurus.
T-Rex had very small forearms, although a few carnivorous dinosaurs such as Carnotaurus had even smaller forearms in proportion to their bodies. There were two digits on each hand.
It’s possible that T-Rexes hunted Alamosaurus, a large sauropod, in packs. This is not proven, but a very plausible theory.
No one knows the coloration of the skin and/or feathers of T-Rex, or whether they were heavily feathered or lightly feathered. It's highly possible that they were more heavily feathered further north, and less so further south where the climate was warmer.