Wright was named to six consecutive Pro Bowls from 1971 to 1976, and in those first three years, he was a First Team All-Pro. His contributions would help Dallas win Super Bowl VI and Super Bowl XII.
Wright left Dallas after being released for the Philadelphia Eagles in 1980, but he never played a game for them, thus making his entire career in the NFL with the Cowboys. He would enter the Pro Football Hall of Fame in 2006, and he is also a member of the 1970s All-Decade Team. Wright was also honored with a place in the Cowboys Ring of Honor in 2004.