Tyrannosaurs are thought to have the most powerful sense of smell out of all dinosaurs, with some having curled tubes of bone inside the nose. These coils most likely would've been covered in a mucus that trapped smells in the nostrils, giving a stronger sense of smell to the animal. T. Rex would have had the second best sense of smell of all the animals at the time, bested only by its earlier ancestor Daspletosaurus. These skills are an aid for both a scavenger & a predator.
T. Rex varies only slightly from the classic large theropods shape; a larger head & jaws in proportion to its body, with smaller arms so the animal would not be unbalanced. Forward facing eyes helped T. Rex judge distances well, & its relation to birds suggest it had good vision, much like modern day humans.
Many of the other members of Tyrannosauridae had feathers, only on hatchlings in the later, larger animals putting Tyrannosaurs firmly into the Coelurusaur family. No T. Rex fossils have been found with feather impressions, but its closest relative; Torosaurus, has been found with feather impressions as hatchlings. Like many dinosaurs closer to birds, T. Rex had a large brain, perhaps the largest of any dinosaur. Casts of the brain-case are as large as a human's, albeit quite a different shape.
T. Rex teeth are like most theropods', serrated. The largest teeth in the mouth were a foot long in most specimens, & are all the same shape. T. Rex replaced its teeth on a regular basis, dropping old teeth with a smaller tooth underneath, much like sharks. The largest most complete fossil find, Sue, measured 12.8 meters (42 feet) long, & 4 meters (13 feet) tall at the hip.