Unlike the ogre, which seems to have a medieval origin, trolls have a pedigree that stretches back into ancient myth. Specifically, they are Scandinavian, where they are nocturnal humanoids, often living out in the wilds and at least suspicious of, if not outright hostile to, humans. Tolkien used them in the way that D&D later went on to use ogres, but retaining the mythic feature of them turning to stone in sunlight.
Many other fantasy works have used trolls in the "large, strong and stupid" role of D&D ogres, with the stone-based giants of Pratchett's
Discworld and the grey-skinned mountain trolls of
Harry Potter being particularly original or well-known examples. The troll of D&D, however, has no real resemblance to these, or to the mythic creature; Gygax instead stated that his inspiration was the 1961 novel
Three Hearts and Three Lions by Poul Anderson, which features a regenerating troll, along with a number of other tropes he adopted for the game.
1E
Trolls are initially shown as cadaverous humanoids with a green or grey warty skin, exaggerated facial features, including a long pointed nose, and writhing tendrils in place of hair. The eyes are large black wells beneath a pronounced brow ridge. Trolls possess no visible genitalia, and so presumably do not reproduce in the human fashion, and have only four digits on their hands and feet - even then one of the toes appears vestigial.
Physically, they are powerful creatures, able to deliver a rapid series of blows, each more powerful than a typical sword-strike, and they have a rubbery hide that's thicker and more resilient than rhino-skin. Even without their regenerative powers, they are about halfway between ogres and the smallest of true giants in their ability to soak up damage - although some of this could be due to simple combat prowess, or a lack of truly vital organs. They also have acute senses, particularly smell (which would explain the large nose).