Trtík was born in Kosice, and started playing handball first for VSZ Kosice, and then also for Banik Karvina and Banik Ostrava.
Following the end of his playing career, he became a successful coach. Twice he led the Czech men's national team. First at the Men’s EHF EURO 2004 and at the 2005 IHF Men’s World Championship in Tunisia.
He assumed the team’s helm a second time from 2021 to February 2022, coaching the team at the Men's EHF EURO 2022.
On club level, he led Frýdek-Místek to the national championship title in 2003. He also managed Slovakian side Tatran Presov, with whom he won the national title three times.
In Germany, he coached MT Melsungen, leading the side from the second division to the Bundesliga in 2005.
The European Handball Federation’s thoughts are with Rastislav Trtik's family and friends at this sad time.