Coming through the youth system, Szoboszlai made his senior debut in 2017 with Austrian club FC Liefering, the reserve team of Red Bull Salzburg.

In July 2023, he joined Liverpool after they paid his release clause of €70 million, making him the club's fourth-most expensive signing of all time.

Szoboszlai made his professional debut in the 2017–18 campaign, playing for the FC Liefering in the second division against Kapfenberg on 21 July 2017.

[27][28] On 2 July 2023, Liverpool signed Szoboszlai on a five-year contract after triggering his release clause which was reportedly worth £60 million.

[31] On 13 August, Szoboszlai made his debut for Liverpool in their opening game of the 2023–24 season as his side drew 1-1 with Chelsea.

[34][35][36] On 3 September 2023, Szoboszlai scored his first goal for Liverpool in a 3–0 Premier League win against Aston Villa, using his weak foot to strike from outside the box in the 3rd minute.

Szoboszlai received his first call-up to the senior Hungary squad for the friendly against Russia and a 2018 FIFA World Cup qualifier against Andorra in June 2017.

[52] On 21 March 2019, Szoboszlai made his first appearance for the Hungarian senior team as a 54th-minute substitute for László Kleinheisler in a UEFA Euro 2020 qualifier against Slovakia.

[56] Despite being initially selected in Hungary's squad for the Euro 2020 finals, Szoboszlai withdrew on 1 June 2021 due to an injury.

[58] After the retirement of Ádám Szalai and long-term injury of Péter Gulácsi, Marco Rossi appointed Szoboszlai as the new captain of the national team in November 2022.

[60] On 27 March 2023, Szoboszlai scored his first goal as captain against Bulgaria in a 3–0 victory for Hungary in the UEFA Euro 2024 qualifying at the Puskás Aréna.

[65] On 15 June, he became the youngest captain to feature in the European competition, aged 23 years and 234 days, in which he provided an assist in a 3–1 defeat against Switzerland in Hungary's opening match of the tournament.

[68] On 19 November 2024, he scored a Panenka penalty kick in the 98th minute in a 1-1 draw against Germany on the last group match of the 2024–25 UEFA Nations League A season.

[71] In an interview published on Nemzeti Sport, his manager, Mátyás Esterházy, said that Szoboszlai is a versatile footballer since he plays different positions in Liverpool and the national team.

[73] He has frequently been compared to compatriot Ferenc Puskás, with Hungarian football pundit Ábel Mészáros saying: "Szoboszlai is ahead of everyone since Lajos Détári.

[77][78] In 2023, he donated a shirt to the foundation that helped to raise money for the family of late Csaba Ponczok, former player of Maglódi TC, who died in 2022.

[81] On 16 October 2024, he announced that he was engaged to Borka Buzsik,[82][83][84][85] a PR manager for the Hungarian company Toman Diet.