The NCAA was without a playoff for the major college football teams in the University Division, later known as Division I-A, during the 20th century. The NCAA recognizes Division I-A national champions based on the final results of polls including the "wire service", FWAA and NFF. The 1964 AP poll continued to rank only ten teams, compiling the votes of 55 sportswriters, each of whom would give their opinion of the ten best. Under a point system of 10 points for first place, 9 for second, etc., the "overall" ranking was determined.
The 1982 NCAA Division I-A football season was the last for Paul "Bear" Bryant as head coach at Alabama, retiring with 323 victories in 38 seasons.
The 1985 NCAA Division I-A football season saw the Oklahoma Sooners, led by head coach Barry Switzer, win the national championship.
The 1983 NCAA Division I-A football season ended with the University of Miami, led by Bernie Kosar, winning their first national championship over perennial power and top ranked Nebraska in the Orange Bowl.
The 1981 NCAA Division I-A football season ended with the Clemson Tigers, unbeaten and untied, claiming the national championship after a victory over Nebraska in the Orange Bowl. This was also the first year of the California Bowl, played in Fresno, California; this game fancied itself as a "junior" version of the Rose Bowl as it pitted the Big West Conference champion vs. the Mid-American Conference champion.
The 1966 University Division football season was marked by some controversy as the year of "The Tie", a famous 10–10 game between the two top-ranked teams, Michigan State and Notre Dame on November 19. Both teams were crowned national champions by various organizations after the regular season concluded, and neither participated in a bowl game. Alabama finished the regular season undefeated and was third in the AP poll, while Georgia was fourth. Alabama went on to win the Sugar Bowl in dominant fashion. During the 20th century, the NCAA had no playoff for the major college football teams in the University Division, later known as Division I-A.
In the 1968 NCAA University Division football season, the system of "polls and bowls" changed. The Associated Press returned to its pre-1961 system of ranking the Top 20 rather than the Top 10, and voted on the national champion after the bowl games, rather than before. During the 20th century, the NCAA had no playoff for the major college football teams in the University Division, later known as Division I-A.
The 1970 NCAA University Division football season was marked by tragedy, due to two airplane crashes. On October 2, one of the planes carrying the Wichita State football team crashed on the way to a game against Utah State, killing 31 people on board, including 14 players. Then, on November 14, the charter for the Marshall Thundering Herd crashed on the way home from a game against East Carolina, killing all 75 persons.
The 1973 NCAA Division I football season was the first for the NCAA's current three-division structure. Effective with the 1973–74 academic year, schools formerly in the NCAA "University Division" were classified as Division I. Schools in the former "College Division" were classified into Division II, which allowed fewer athletic scholarships than Division I, and Division III, in which athletic scholarships were prohibited.
The 1976 NCAA Division I football season ended with a championship for the Panthers of the University of Pittsburgh. Led by head coach Johnny Majors, the Pitt Panthers brought a college football championship to the home of the defending pro football champions, the Steelers. Pitt also had the Heisman Trophy winner, Tony Dorsett; the Panthers had been ranked ninth in the preseason AP poll.
The 1977 NCAA Division I football season was one in which the top five teams finished with 11–1 records. Notre Dame, which beat top-ranked and undefeated Texas in the Cotton Bowl, became the national champion.
The 1929 college football season saw a number of unbeaten and untied teams. Purdue, Tulane, Notre Dame, and Pittsburgh all finished the regular season with wins over all their opponents. Notre Dame was recognized as national champion by all three of the contemporary major selectors. Houlgate would later name USC (10–2) on the basis of post-season play. Eight of nine retrospective selectors later also named Notre Dame and USC as No. 1 teams.
The 1935 college football season was the last one before the Associated Press (AP) writers' poll was used in selecting the national champion. There were seven contemporary math system selectors that year who are informally recognized by the NCAA as "nationwide in scope". The Dickinson System, run by University of Illinois Professor Frank Dickinson, selected Southern Methodist University (SMU) as best in the nation. The Houlgate System, created by Carroll Everard "Deke" Houlgate Sr., also selected SMU. The contemporary Boand, Litkenhous and Poling math rating systems all selected Minnesota as the No. 1 team in the nation. The Dunkel System selected Princeton as its top team. The Williamson System, by Paul O. Williamson of New Orleans, ranked Texas Christian University first.
The 1952 college football season was the 84th season of intercollegiate football in the United States. It ended with Oklahoma halfback Billy Vessels winning the Heisman Trophy and Notre Dame halfback Johnny Lattner winning the Maxwell Award. Two teams claim the 1952 national championship:
The 1951 college football season was the 83rd season of intercollegiate football in the United States. It finished with Princeton halfback Dick Kazmaier winning the Heisman Trophy and the Maxwell Award. Five teams have laid claim to the 1951 national championship:
The 1948 college football season finished with SMU halfback Doak Walker as the Heisman Trophy winner and six teams in contention for the national championship:
- Bennie Oosterbaan's Michigan compiled a 9–0 record, defeated six ranked opponents, and was the consensus national champion, receiving 192 of 333 first-place votes in the final AP Poll. It was Michigan's second consecutive undefeated season, extending the program's winning streak to 23 games.
- Frank Leahy's Notre Dame Fighting Irish compiled a 9–0–1 record and had a 21-game winning streak dating back to the 1946 season before playing a 14–14 tie with USC in the final game of the 1948 season. Notre Dame was ranked No. 2 in the final AP Poll, receiving 97 of 333 first-place votes, with the same record as Michigan due to the final poll being taken prior to their season-ending tie.
- Carl Snavely's No. 3 North Carolina Tar Heels, led by Heisman Trophy runner-up Charlie Justice, were undefeated in the regular season (9–0–1) but lost to Oklahoma in the 1949 Sugar Bowl.
- Pappy Waldorf's No. 4 California Golden Bears, led by Jackie Jensen who finished fourth in the 1948 Heisman Trophy voting, were undefeated in the regular season (10–0), but lost to Northwestern in the 1949 Rose Bowl.
- Bud Wilkinson's No. 5 Oklahoma Sooners compiled a 10–1 record, including a victory over No. 3 North Carolina in the 1949 Sugar Bowl.
- Earl Blaik's No. 6 Army Cadets finished the season undefeated (8–0–1). They won the first eight games of the season and were ranked No. 3 in the AP Poll before playing Navy to a tie in the annual Army–Navy Game.
The 1946 college football season was the 78th season of intercollegiate football in the United States. Competition included schools from the Big Ten Conference, the Pacific Coast Conference (PCC), the Southeastern Conference (SEC), the Big Six Conference, the Southern Conference, the Southwestern Conference, and numerous smaller conferences and independent programs. The season saw the return of many programs which had suspended play during World War II, and also the enrollment of many veterans returning from the war.
The 1938 college football season ended with the Horned Frogs of Texas Christian University (TCU) being named the nation's No. 1 team by 55 of the 77 voters in the final Associated Press writers' poll in early December. Tennessee was also chosen by six contemporary math system selectors as a national champion; both teams won every game. Notre Dame was chosen by the Dickinson System and won the Knute Rockne Memorial Trophy.
The 1939 college football season concluded with the Aggies of The Agricultural and Mechanical College of Texas being named as the national champions by the voters in the Associated Press writers' poll. Led by consensus All-American fullback John Kimbrough, the Aggies went undefeated at 11–0 and outscored their opponents by a combined total of 212 to 31, with the defense allowing just 54 first downs and 763 yards all season, or 1.71 yards per play. On New Year's Day, Texas A&M defeated Tulane, 14–13 in the Sugar Bowl.
The 1943 college football season was the 75th season of intercollegiate football in the United States. Played during World War II, the competition included schools from the Big Ten Conference, the Pacific Coast Conference (PCC), the Southeastern Conference (SEC), the Big Six Conference, the Southwestern Conference, and numerous smaller conferences and independent programs.