World Championships

Solís became world champion in 2001 in Belfast and in 2003 in Bangkok at heavyweight (201 lbs/91 kg limit), in 2005 in Mianyang at super heavyweight.

In 2001 he beat Russian Olympic silver medalist of 2000 Sultan Ibragimov in the semifinals on points and in the final British David Haye by TKO. Haye gave Solis a standing eight count in the first round and was up by 7 points, but Solis came back strong, turned the score around in the second round and won the fight by stoppage in the third. At the time of stoppage, score was 31–17 in favour of Solis.

In 2003 he won on points in the final against Russian archrival Aleksandr Alekseyev who would win the next world championship. Also, Solis defeated Sultan Ibragimov once more (13-7) in four rounds in the XXXIII Chemistry Cup in Halle, Germany, on March 10, 2002.

Olympic Games

Solis earned a spot on the Cuban Olympic boxing team for the 2004 Summer Olympics in Athens and succeeded the three-time champion Savon as the heavyweight gold medalist.

Amateur highlights

Solís vs. Barrett

Solis fighting out of Miami, Florida, made his third successful defense of the WBC International Heavyweight title with a second round stoppage of Monte Barrett of Queens, New York. Solis, now 15–0 with 11 KOs, a Cuban defector with an extensive amateur career, fought a very cautious first as a careful counterpuncher, preferring to feel out the experienced Barrett, age 38, 34–8, 20 KOs, to see if he had anything left. In the second, Solis opened up with a long left to Barrett's chin that decked him. Barrett just beat the count. In the barrage from Solis that followed, Barrett went down from a slip under pressure, got up, then got knocked out.

Solís vs. Drumond

On 20 March 2010, Solis fought and defeated Carl Davis Drumond by fourth-round TKO to retain his WBC International Heavyweight title and to win the WBA Fedelatin Heavyweight title. After toying with Drumond for the first three rounds Solis unleashed a barrage of punches during the last 20 second of round three and would have knocked Drumond down had he not been saved by the ropes, making Drumond not want to come out for the fourth round.

Solís vs. Vitali Klitschko

Solis defeated Ray Austin in a WBC title eliminator when Austin was disqualified in the 10th round. Solis connected with combinations to the head in the 10th, with Austin seemingly out on his feet and repeatedly holding Solis to avoid additional shots. The win set up Solis to fight Vitali Klitschko, becoming the mandatory challenger.^[2][3] On 11 January, it was official confirmed that the fight between Vitali Klitschko and Solís was going to take place in Cologne, Germany, on 19 March 2011. Both fighters promised a victory by knockout.

On 19 March 2011, the two boxers took to the ring in front of a sell-out crowd of over 19,000. In the first round of the fight, after the ten-second warning bell rang, Solis threw a left and right which didn't connect, to Klitschko's chin. Vitali Klitschko returned the favor with a short right to Solis's left temple. What followed has been extensively debated by fans and pundits. Some claim that as he was already falling to the ground, Solis injured his right knee while making an effort to prevent himself from hitting the ground. Others maintain that he simply injured his knee, while backpedalling, and was unable to continue. Some believe he was injured prior to the bout but didn't disclose it for fear of not getting paid. The slow motion shows that he was momentarily stunned by the almost grazing temple punch, and his foot froze to the canvas, whilst his leg and body continued backwards, causing an injury to his ankle. He was not able to continue and the fight was ruled a 1st rd KO.

Post Klitschko comeback

Solis launched a comeback following his rehabilitation from knee surgery and scored three consecutive victories over the next three years including points wins over Konstantin Airich and undefeated prospect Leif Larsen. Problematically though it seemed Solis had lost a certain amount of his punching power and foot speed.

Consecutive losses and decline

In 2015 Solis lost two consecutive bouts to former world title challenger, veteran, Tony Thompson. The first was by a close split decision and the second by TKO as Solis retired in his corner for reasons unknown midway through the bout. Since his losses to Thompson Solis has won two bouts against low level opposition. His current ranking according to boxrec is 42 in the world and there has been no speculation regarding a substantive ring return.