The 1957 NCAA University Division football season saw two different national champions. Auburn was ranked first in the AP writers' poll taken at season's end, while Ohio State was first in the UPI coaches' poll. Auburn was ineligible for a bowl game, however, having been placed on probation indefinitely by the Southeastern Conference, after having paid two high school players $500 apiece.
The 1926 college football season was the first in which an attempt was made to recognize a national champion after the season.
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 under the Dickinson System and by a United Press writer while Pitt was considered a national champion by several others due to Pitt possessing a greater scoring differential over the two teams' only common regular season opponent. Following the season, Pitt traveled to Pasadena to meet USC in the Rose Bowl, at that time the only postseason college football game and held between the perceived best teams of east and west. Despite Pitt's losing 47–14 to the Trojans, as bowls were still considered exhibitions by many, college football historian Parke H. Davis, whose national championship selections are recognized by the official NCAA records book, named the Panthers as that season's national champion while several other retroactive selectors recognized by the NCAA records book have selected Notre Dame. Both Notre Dame and Pitt claim a national championship for the 1929 season and both are recognized in the NCAA Records Book and by College Football Data Warehouse.
The 1930 college football season saw Notre Dame repeat as national champion under the Dickinson System, and a post-season Rose Bowl matchup between two unbeaten (9–0) teams, Washington State and Alabama, ranked No. 2 and No. 3, respectively. Alabama won the Pasadena contest, 24–0.
The 1931 college football season saw the USC Trojans win the Knute Rockne Memorial Trophy as national champion under the Dickinson System. Rockne, who had coached Notre Dame to a championship in 1930, had been killed in a plane crash on March 31, 1931. For the first time, the champion under the Dickinson system also played in a postseason game. The Rose Bowl, promoted as an unofficial championship matchup between the best teams of East and West, matched USC and Tulane, No. 1 and No. 2 in the Dickinson ratings. USC won, 21–12. Also for 1931, historian Parke Davis, through research, selected Pittsburgh and Purdue as National Champions and these selections, along with USC, are all recognized by the official NCAA records book. Both USC and Pitt claim national championships for 1931, and both are recognized by College Football Data Warehouse.
The 1932 college football season saw the Michigan Wolverines win the Knute Rockne Memorial Trophy as national champion under the Dickinson System. Because the "Big Nine" conference didn't permit its teams to play in the postseason, however, the Wolverines were not able to accept a bid to the Rose Bowl. As such, the Pasadena game matched the No. 2 and No. 3 teams, USC and Pittsburgh, with the USC Trojans winning the East-West matchup 35–0.
The 1935 college football season was the last one before the Associated Press writers' poll was used in selecting the national champion. The Williamson System, calculated by Paul O. Williamson out of New Orleans, deemed Texas Christian University (TCU) as the best in the nation. The Dickinson System, consisting of the calculations of University of Illinois Professor Frank Dickinson, crowned Southern Methodist University (SMU) as the best in the nation. A poll of newspaper writers, taken at year's end—by United Press rather than the AP—concluded that Minnesota was the best in the nation.
The 1936 college football season was the first in which the Associated Press writers' poll selected a national champion. The first AP poll, taken of 35 writers, was released on October 20, 1936. Each writer listed his choice for the top ten teams, and points were tallied based on 10 for first place, 9 for second, etc., and the AP then ranked the twenty teams with the highest number of points. In the first poll, Minnesota received 32 first place votes, and 3 votes for an additional 25 points, for a total of 345 altogether.
The 1925 college football season ended with no clear national champion. At the close of the season, noted sports writer Billy Evans described the championship contest as "a dead heat" among Dartmouth, Tulane, Michigan, Washington, and Alabama.
The 1924 college football season was the year of the Four Horsemen as the Notre Dame team, coached by Knute Rockne, won all of its games, including the Rose Bowl, to be acclaimed as the best team in the nation. Notre Dame and Stanford were both unbeaten at season's end, with the Fighting Irish winning the Rose Bowl contest 27–10. The Penn Quakers were retroactively awarded a national championship by Parke H. Davis.
The 1923 college football season saw several teams finish their seasons unbeaten and untied. As such, numerous schools claim a national championship for the 1923 season. Illinois and Michigan, both members of what is now the Big Ten Conference, finished with records of 8–0 and were selected as national champion by multiple selectors. Illinois featured break-out star Red Grange. Ivy League teams Yale and Cornell also had undefeated seasons.
The 1949 college football season finished with four teams that were unbeaten and untied-- Notre Dame, Oklahoma, California, and Army had won all their games at season's end. Notre Dame, however, was the overwhelming choice for national champion in the AP Poll, with 172 of 208 first place votes. The Fighting Irish did not participate in the New Year's Day bowl games, which were played on January 2, 1950.
The 1947 college football season finished with Notre Dame, Michigan and Penn State all unbeaten and untied, but the Fighting Irish of Notre Dame were the first place choice for 107 of the 142 voters in the AP Poll, and repeated as national champions. Michigan went on to meet USC in the Rose Bowl and won 49–0, while Penn State was tied 13–13 by SMU in the Cotton Bowl Classic, and Notre Dame didn't participate in the postseason. An unofficial post bowl AP poll was conducted with Michigan and Notre Dame as the only options and Michigan won by a vote of 226 to 119.
The 1937 college football season ended with the Panthers of the University of Pittsburgh being named the nation's No. 1 team by 30 of the 33 voters in the Associated Press writers' poll. The AP poll was in its second year, and seven votes were taken during the final weeks of the 1937 season, starting with October 18. Each writer listed his choice for the top ten teams, and points were tallied based on 10 for first place, 9 for second, etc., and the AP then ranked the twenty teams with the highest number of points. With 33 writers polled, Pitt received 30 first place votes and 3 second-place, for a total of 327 points.
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.
The 1940 college football season ended with the Gophers of the University of Minnesota being named the nation's No. 1 team and national champion by the AP Poll, and the Stanford University Indians in second, with the two teams receiving 65 and 44 first place votes respectively. Each writer listed his choice for the top ten teams, and points were tallied based on 10 for first place, 9 for second, etc., and the AP then ranked the twenty teams with the highest number of points. Minnesota, Stanford, Boston College, and Tennessee all claim 1940 as a national championship season.
The 1941 college football regular season was the 73rd 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.
In 1942, Ohio State and Georgia were crowned national champions. Georgia defeated UCLA in the Rose Bowl on January 1, 1943. Nine ranking authorities listed in the NCAA record books listed the Bulldogs as No. 1. Ohio State was crowned No. 1 in the final AP Poll at the end of November and did not make a bowl appearance. At the time, the AP poll did not put out a post-bowl poll.
The 1943 college football season concluded with the Fighting Irish of Notre Dame crowned as the nation's No. 1 team by a majority of the voters in the AP Poll, followed by the Iowa Pre-Flight Seahawks as the runner-up. For the third time in the history of the AP Poll, a team that had lost a game was named mythical national champion;. Notre Dame lost its final game of the season, a Chicago contest against the Great Lakes Naval Training Center. Along the way, however, the Fighting Irish had played one of the toughest college schedules ever, beating two No. 2 ranked teams and two No. 3 ranked teams. Purdue University would seemingly have a claim on the 1943 Championship as well as the only undefeated team playing a full schedule, but the Purdue athletic department has never pursued the claim.
The 1945 college football season finished with the undefeated United States Military Academy, more popularly known as "Army", being the unanimous choice for the nation's number one team by the 116 voters in the Associated Press writers' poll. The runner up was the undefeated Alabama Crimson Tide, followed by the United States Naval Academy, more popularly known as "Navy". In 2016, the American Football Coaches Association retroactively named the Oklahoma A&M Cowboys national champion for 1945.