NCAA Football Seasons Year, National Champion, Heisman Trophy . College Football Scores · Most Recent Games and Any Score Since. Complete history of NCAA Football Champions. From the days of #1 ranked teams (sometimes 2 in a year) to the BCS to the College Football Playoffs starting in. The BCS National Championship Game, or BCS National Championship, was a postseason college football bowl game, used to determine a national champion of the NCAA Division I Football Bowl Although in most years the winner of the BCS National Championship would also be designated as the national champion History · Game results · Heisman Trophy winners · Criticisms and controversy.