[7] In 2006, Pešta started training Traditional Musado under the leadership of Vít Skalník.
[9] In 2008, he started training MMA under the leadership of Jiří Vesecký in the gym in Příbram, Bohemia.
[6] Pešta made his debut against face fellow newcomer Ruslan Magomedov on May 31, 2014 at UFC Fight Night 41.
[12] For his second fight with the promotion, Pešta faced touted newcomer Konstantin Erokhin on January 24, 2015 at UFC on Fox 14.
[18] Pešta was expected to face Damian Grabowski on January 15, 2017 at UFC Fight Night 103.
[19] However, Grabowski pulled out of the fight in late December for undisclosed reasons and was replaced by Alexey Oleynik.
He signed a contract with Fight Nights Global in the second part of year 2017 after one match at home organization XFN.
[30] Pešta faced Szymon Bajor on December 16, 2023 at KSW 89: Bartosiński vs. Parnasse, losing the bout via split decision.
[31] Pešta's signature move, the (side) mounted crucifix position, was nicknamed/called "Bába pod kořenem (English: The crone under the root)" by his fans, after the famous Czech TV Nova's report about an elderly woman who gets stuck for 11 hours under the root of a tree overnight, 50 meters away from her rented hut in the forest and her friends.