Yale has 18 national championships that are recognized by the NCAA. The Bulldogs have the most…read moretitles of any college football program in history. That said, those championships were won a long time ago, before the modern era: 1874, 1876, 1877, 1880, 1881, 1882, 1883, 1884, 1886, 1887, 1888, 1891, 1892, 1894, 1900, 1907, 1909, and 1927.
Yale and the other Ivy League football teams moved down to NCAA Division I-AA in 1982 (I-AA's first season was in 1978). Since 2006, I-AA officially became known as the Division I Football Championship Subdivision (FCS). Again, a step below where the bigger programs reside. For example, Alabama, Notre Dame, Michigan, and Southern California play in the Football Bowl Subdivision (FBS). Before college football grew and evolved into what it is today, Yale was king.
An important distinction to make between Ivy League football programs and FBS programs is no school from the Ivy League awards football scholarships. However, student-athletes can receive needs-based scholarships in the Ivy League. In general, Yale and the other Ivy League football schools have significantly smaller programs when compared to those in the FBS, hence their classification as FCS members.
Since joining the Ivy League in 1956, Yale has won 16 conference championships. Unlike FBS conferences where there is a conference championship game, the Ivy League has no such thing. Therefore, it is possible to have co-champions in the league. Five of Yale's last six conference titles were shared. Since becoming the current Bulldogs head coach in 2012, Tony Reno has been responsible for two of those championships: 2017 outright (9-1 overall, 6-1 Ivy) and 2019 co-champions with Dartmouth (both schools went 9-1 overall, 6-1 Ivy).
I'm not sure the reasons why, but the Ivy League chooses not to participate in the NCAA Division I Football Championship playoffs. Therefore, they do not presently have the opportunity to compete for national championships that are sanctioned and recognized by the NCAA.
Yale's home football stadium, the Yale Bowl, is the biggest in the Ivy League with a seating capacity of 61,446. Opened in 1914, it's the third-oldest venue in the conference. It is located west of Yale's main campus, on the other side of Ella T Grasso Blvd, with some of the school's other athletic facilities such as Reese Stadium (soccer) and the tennis complex.