He was drafted by Miami in the 8th round of the 1979 NFL Draft. He became a starter in his rookie year, and continued to start until the end of his career. In 1980, he led the NFL with four fumble recoveries. He played in the Super Bowl twice, in 1983 and 1985, but lost both games. He was a Dolphins nominee for the NFL Man of the Year and for the Ed Block Award for inspiration, sportsmanship and courage. His brother Lyle Blackwood also played in the NFL, and they were teammates from 1981 through 1986 with the Miami Dolphins. On a Monday night game against Buffalo in 1981, Glenn at strong safety and Lyle at free safety ganged up to put some heavy hits on the Bills’ players, prompting a Miami sportswriter to dub them "The Bruise Brothers." The moniker stuck. Blackwood finished his career with 29 interceptions and 13 fumble recoveries. Blackwood was named to the Dolphins' 50 best players in their first 50 seasons in 2015.
