That would be in the 2007-2008 season when they started off 20-0 and eventually rolled on to be the national champions, defeating the Memphis Tigers 75-68 in overtime. The 2008 national championship game was memorable due to "Mario's Miracle," when Mario Chalmers hit the game-tying three pointer as regulation time was nearing zero. The Tigers were the heavy favorite, featuring Derrick Rose amongst others on a team that was the only men's division I College Basketball team to ever reach 38 wins or more in a season (they finished 38-2, with their last lost coming against Kansas).
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The last time they played was a regular season game 1993. Kansas beat Wichita State 103-54.
The last time they played in the NCAA tournament was 1981, Wichita State beat Kansas 66-65.