Matthews is one of four Morris Trophy winners to be enshrined in the Pro Football Hall of Fame in Canton, Ohio. A three year letterman at USC (1980, 81, 82) he played on the same offensive line as two time Morris Trophy winner Roy Foster. He was a captain on the 1982 USC team and was inducted into the USC Hall of Fame in 2005. He was selected in the first round by the Houston Oilers as the ninth overall pick in the 1983 NFL draft. He spent his entire NFL career with the Oilers/Titans and started 229 consecutive games for them. He played in a record 14 Pro Bowls and was an All Pro nine times. His brother Clay as well as three sons, two nephews, and his father all played in the NFL.