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 1984 NCAA Division I-A football season was topsy-turvy from start to finish. It ended with the BYU Cougars being bestowed their first and only national championship by beating Michigan in the Holiday Bowl. While the Cougars finished with a perfect 13–0 record and were the consensus National Champions, some commentators maintain this title was undeserved citing their weak schedule and argue that the championship should have gone to the 11–1 Washington Huskies. Despite this the Cougars were voted No. 1 in the final AP and UPI polls. The Huskies declined an invitation to play BYU in the Holiday Bowl; they decided instead to play Oklahoma in the more prestigious 1985 Orange Bowl. All subsequent national champions have come from what are now known as the Power Five conferences + Notre Dame.
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 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 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 1974 NCAA Division I football season finished with two national champions. The Associated Press (AP) writers' poll ranked the University of Oklahoma, which was on probation and barred by the NCAA from postseason play, No. 1 at season's end. The United Press International (UPI) coaches' poll did not rank teams on probation, by unanimous agreement of the 25 member coaches' board. The UPI trophy went to the University of Southern California (USC).
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 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 1954 college football season saw three teams finish unbeaten and untied, with Ohio State Buckeyes and the UCLA Bruins sharing the national championship as the No. 1 picks of the AP Poll and the UPI Poll, respectively. Although the winners of the Big Ten and the Pacific conferences normally met in the Rose Bowl, a "no repeat" prevented the two champions from meeting. UCLA, which had been in the Rose Bowl earlier in the year, was replaced by conference runner-up USC.
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 1952 college football season ended with the unbeaten Michigan State Spartans (9–0) and Georgia Tech Yellow Jackets (12–0) each claiming a national championship from different polls. Michigan State finished first according to two of the "wire service" polls, which both placed Georgia Tech second. Georgia Tech was first in the International News Service poll. UP and INS merged in 1958 to form UPI. Although the Spartans became members of the Big Ten Conference in 1950, full participation did not come until 1953, and under the terms of their entry into the conference, they were not allowed to participate in postseason play. Georgia Tech won the Sugar Bowl on New Year's Day in New Orleans.
The 1951 college football season finished with seven unbeaten major college teams, of which five were unbeaten and untied. Ultimately, the Tennessee Volunteers were voted the best team by the Associated Press, followed by the Michigan State Spartans, with the Vols having a plurality of first place votes. Tennessee lost in the Sugar Bowl to the equally undefeated and untied No. 3 Maryland Terrapins, but the postseason games were not taken into account by the major polls. Tennessee, Maryland, Michigan State, and Illinois all claim national championships for 1951.
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 1946 college football season finished with the Notre Dame Fighting Irish crowned as the national champion in the AP Poll, the Georgia Bulldogs recognized as national champion by the Williamson poll and United States Military Academy named as national champion in various other polls and rankings. The Delaware Fightin' Blue Hens were recognized by the AP as the small college national champion. Notre Dame and Army both won all of their games, with the exception of their November 9 meeting at New York's Yankee Stadium, where they had played to a 0–0 tie in a No. 1 vs No. 2 matchup regarded as a "Game of the Century". Neither team played in bowl game that season.
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.