Oscar has a green body (during the 1969–1970 season, however, he was orange), has no nose, and lives in a garbage can. His favorite thing in life is trash; evidence for this is the song "I Love Trash". He's known as "The Grouch" because of his typically grouchy moods, which tend to be on the whiney side, although he can also be very clever, as well as being of the grouch species. Some say he is very smart.

Oscar can also become mobile with the help of his friend Bruno, the trashman, who carries Oscar around in his can. Bruno is a full-body costume which allows Oscar's puppeteer to manipulate Oscar while remaining hidden by the Bruno costume. Also, as seen in the Elmo's World episode 'Dance', the underside of his trash can is somewhat detachable, with Oscar's legs protruding from the bottom of his trash can. Other evidence of this can be seen in Christmas Eve on Sesame Street (1978), when Oscar is ice skating. For several seasons, Oscar was frequently shown with his friend and pet Slimey, an orange worm. On occasional episodes he has mentioned leaving Sesame Street to attend "the annual Grouch convention in Syracuse, New York".

Oscar is performed by Muppeteer Carroll Spinney. Spinney's other lead character is Big Bird. During the first season of Sesame Street, the street set was arranged such that Spinney, who is right-handed, was forced to operate Oscar's head with his left hand. A subsequent redesign of the set allowed Spinney to switch hands.

Oscar thinks that numbers are silly, according to the song "Knock Three Times".