The film begins with Cassius Clay, Jr. before his championship debut against then heavyweight champion Sonny Liston. In the pre-fight weigh-in Clay heavily taunts Liston (such as calling Liston a "big ugly bear"). In the fight Clay is able to dominate the early rounds of the match, but halfway through he complains of a burning feeling in his eyes (implying that Liston has tried to cheat) and says he is unable to continue. However, his trainer/manager Angelo Dundee gets him to keep fighting. Once Clay is able to see again he easily dominates the fight and right before round seven Liston quits, making Clay the second youngest heavyweight champion at the time after Floyd Patterson. Clay spends valued time with Malcolm X and the two decide to take a trip to Africa.
Clay is then invited to the home of Nation of Islam leader Elijah Muhammad where he is granted the name Muhammad Ali due to his status of World Heavyweight Champion. His father, Cassius Clay Sr. disapproves of this. Ali marries Sonji Roi, an ex-Playboy Bunny, despite her not being Muslim and not abiding by sex segregation. While at home with his wife and children, Malcolm X is called by the Nation of Islam and is informed that his suspension has been extended and Ali will not go to Africa. However, Ali takes the trip to Africa where he finds Malcolm X, but later refuses to speak to him, honoring the wishes of Elijah Muhammad. He is extremely distraught when Malcolm is later assassinated.
Upon returning to America, Ali goes against Sonny Liston a second time and knocks him out in the first round. He and Sonji divorce after she continually objects to certain obligations Muslim women have, notably wearing a hijab.
After being officially called to fight in the Vietnam War with the U.S. Army, Ali refuses, and is subsequently stripped of his boxing license, passport and title, additionally facing five years in prison. Ali marries 17-year-old Belinda Boyd. After a three-year hiatus, his conviction is later overturned and in his first fight in his comeback, he fights Jerry Quarry and wins by technical knockout in three rounds when Quarry gets a cut in his eye.
Ali attempts to regain the Heavyweight Championship against Joe Frazier. Dubbed the Fight of the Century, Frazier has the upper hand against Ali for most of the rounds. In the fifteenth round, he defeats Ali by decision, giving Ali the first loss of his career. When Frazier loses the championship to George Foreman, Ali makes a decision to fight Foreman and become the first boxer to win his title a second time.
Foreman and Ali go to Kinshasa, Zaire for the Rumble in the Jungle fight. While there, Ali meets a woman named Veronica PorchĂŠ, and has an affair with her. After reading rumors of his infidelity through newspapers, his wife Belinda travels to Zaire to confront him about this. Ali says he is unsure as to whether he really loves Veronica or not, and just wants to focus on his upcoming title shot.
For a good portion of the fight against Foreman, Ali leans back against the ropes and covers up, letting Foreman wildly throw punches at him. During the fight, Ali realizes that he has to react sooner or else he will be knocked out or possibly die in the ring. As the rounds go on, Foreman tires himself out and Ali takes advantage. He quickly knocks out the tired Foreman, and the film ends with Ali regaining the Heavyweight Championship of which he was previously stripped.

Question: Why was Liston suspected of cheating?
Answer: Cassius Clay Jr's eyes started to burn
Alternative answer: Clay has a burning feeling in his eyes after boxing a few rounds.