Martin became known for scoring defensive touchdowns, which is not-so-common for a defensive lineman. Over his NFL career with New York, he notched six non-offensive touchdowns. He was also credited with a receiving touchdown in 1980. As noted on wikipedia:
"Martin's 7 NFL TDs came on 3 interception returns, 2 fumble returns/recoveries, one lateral return following a blocked field goal, and one offensive pass reception (in 1980, lining up as a tight end). (In November 2006, Miami's All-Pro defensive end Jason Taylor broke Martin's career record by notching his 7th defensive touchdown after intercepting a Brad Johnson pass.)".
During his time as a Giant, Martin racked up 7 touchdowns, 46 sacks (which only became an official statistic in 1982), and 15 fumbles returned.
The impact that Martin had as a New York Giant, particularly during their first Super Bowl Championship following the 1986 season, can be summed up by noting that of all the players who passed through the coaching career of Bill Parcells, Martin was chosen by Parcells to induct him into the Pro Football Hall of Fame.