[5] While he was still a cadet, Szilágyi joined the senior Hungarian team for the 2007 World Fencing Championships in Saint-Petersburg.

For this performance, Tamás Decsi, Balázs Lontay, Zsolt Nemcsik and Áron Szilágyi were named Hungarian team of the year.

In the table of 16 he defeated 2008 Olympic champion Zhong Man of China, then overcame Germany's Max Hartung and Russia's Nikolay Kovalev to reach the final.

After taking an early 7-0 lead over Italy's Diego Occhiuzzi, Szilágyi closed the match on 15–8 to win Hungary's first gold medal in the London games.

[7] Szilágyi featured on the official poster and video campaign of the 2013 World Fencing Championships held in his home city, Budapest.

In the 2014–15 season Szilágyi claimed his first continental title in Montreux, after prevailing over Max Hartung despite a right-ankle injury.

[2] He won the gold medal in the men's sabre event at the 2022 World Fencing Championships held in Cairo, Egypt.

In 2021, he accepted the invitation to become Social Chairman of the Forum for the Protection of Interests of Hungarian Elite Athletes.