In the video player above, Eyewitness Sports' Leslie Hill follows the team to New Orleans, when they went to the Final Four in 1982.
That team featured Clyde Drexler and Hakeem Olajuwon, a freshman at the time.
Speaking of Olajuwon, another video from the ABC13 archives features an interview with UH Hall of Fame coach Guy V. Lewis and Hakeem, known as Akeem at the time, at the Southwest Conference tournament in 1982 before the squad made the run to the Final Four that year.
But Olajuwon hadn't even seen his first basketball game until 1979, he explained in the footage below.
In the Phi Slama Jama days of the early '80s, the Coogs made three straight Final Four appearances from 1982-84. Twice, the team advanced to the National Championship game.
Now Houston has another shot at trying to bring home a title.
But first, the Coogs will have to get past the formidable Baylor Bears this weekend.
Their Texas showdown is set for 4:14 p.m. Saturday at Lucas Oil Stadium in Indianapolis.
Texas showdown: University of Houston and Baylor set to battle in Final Four