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 1958 NCAA University Division football season was notable in that it was the first to feature the two-point conversion. On January 13, 1958, the eleven-man NCAA Rules Committee unanimously approved a resolution to allow teams to choose between kicking an extra point after a touchdown, or running or passing from the three-yard line for two points. University of Michigan athletic director Fritz Crisler said at the meeting in Fort Lauderdale, "It's a progressive step which will make football more interesting for the spectators," adding that the rule "will add drama to what has been the dullest, most stupid play in the game."
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 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 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 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 1956 NCAA University Division football season saw the University of Oklahoma Sooners finish a third consecutive season unbeaten and untied to again win the national championship.
The 1955 college football season saw the Oklahoma Sooners win the national championship after going 10–0–0. Although the final poll was taken before the postseason bowl games, Oklahoma played against the nation's other unbeaten and untied (10–0–0) team, the Maryland Terrapins, at the Orange Bowl in Miami, and won 20–6.
The 1953 college football season finished with the Maryland Terrapins capturing the AP, INS, and UPI national championship after Notre Dame held the top spot for the first nine weeks. The No. 4 Oklahoma Sooners defeated Maryland in the Orange Bowl, but there was no further polling after the November 30 results were released. However, Notre Dame was selected as the National Champions by 10 other polls and the Oklahoma Sooners received first in two polls. However, despite the team receiving National Championship rings, the University of Notre Dame does not recognize this title due to their policy of only recognizing AP or coaches' poll titles during the polling era (1936–present). Maryland was also the first champion of the Atlantic Coast Conference, which had been formed earlier in 1953 by seven colleges formerly with the Southern Conference. The year 1953 also saw the Michigan State Spartans, previously an independent, join the Big Nine Conference, which then became the Big Ten; MSU won the conference title in that first year and was the conference representative to the Rose Bowl, which it won 28–20 over UCLA.
The 1950 college football season finished with the unbeaten and untied Oklahoma Sooners (9–0) being the consensus choice for national champion. On New Year's Day, however, the Sooners were upset by the Kentucky Wildcats in the Sugar Bowl. The Army Cadets, ranked No. 2 in the AP Poll, had been defeated in their final regular season game by 2–6 Navy, 14–2. However, the final poll had been issued on November 27, and the bowl games had no effect on Oklahoma's status as the No. 1 team.
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 1948 college football season finished with two unbeaten and untied teams; Michigan and Clemson. Michigan was the first place choice for the majority voters in the AP Poll, but didn't play in the postseason because of a no-repeat rule for Big Nine schools. Notre Dame, second in the AP Poll, tied USC 14–14 at the end of the regular season, but did not participate in any bowl per university policy at the time. Northwestern beat California 20–14 in the Rose Bowl, and Clemson defeated Missouri by a point in the Gator Bowl.
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 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 is also recognized as a national champion; both teams won every game.
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.
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.