All of Iowa's titles are from the Dark Ages of College Football and none of them were ever conferred by a major source like the AP Poll, Coaches Poll, etc., and they all pre-date any of the Bowl Alliance / BCS / CFP era. The 1921-1922 championships are ancient, and as my earlier "forward pass" joke goes, not completely that much off base. The forward pass was legalized in 1906. Two-Platoon football wasn't even the norm until the 1940s.
Moving onto the 1956 and 1958 titles. Iowa did at least win the Big Ten in those years, but they finished with dual rankings from the AP/Coaches of 3/3 (1956) and 2/2 (1958). More convincingly, Bud Wilkinson's Oklahoma took home the AP & Coaches titles in 1956, and LSU did the same in 1958 with an undefeated season under Paul Dietzel. At best, Iowa could claim these titles like Michigan claims 1997.
Finally, their 1960 championship is totally dubious. Iowa shared the Big Ten title with Minnesota that year, and the Gophers actually went to the Rose Bowl. Remember that for decades, the Big Ten allowed ONLY their champion to attend the Rose Bowl - while all other teams did not receive bowl bids of any kind. Which of course means that somehow Iowa claims a title while they didn't even go to a bowl game.
(Side note, this is why I say Nebraska should claim all our other undefeated seasons as titles. Freaking Iowa gets away with this crap. So should we. Minnesota claims like 947 titles from back when dinosaurs roamed the earth. It would boost us up to like 9 titles.)
On the conference level, Iowa has won only 4 conference titles in my lifetime and only one of those (1985) was uncontested. I guess you can put 'em up there with the 1985 Bears. Irrelevant ever since.
- In 1985, they took home the Big Ten title and got shellacked by UCLA in the Rose Bowl.
- In 1990, they shared the B1G title with UM, MSU and Illinois, so I guess 40% of the league was a champ that year. Cool.
- In 2002, they played a solid season with losses only to ISU and USC in the Orange Bowl. Blind squirrels still get some nuts, I guess.
- In 2004, they again shared the title with Michigan, but won a solid game over JaMarcus Russell's LSU. Side note, Russell is the only QB I've ever seen who's fatter than his OL.
† Co-championship