The Croatian War of Independence halted a promising season for the 21-year-old, eventually resulting in Šuker's move to Spanish club Sevilla in 1991.

In La Liga, Šuker was highly regarded, showing consistent form with Sevilla and being consecutively amongst the division's top goal scorers.

The crowning moment of Šuker's career was the 1998 FIFA World Cup in France, where he won the Golden Boot by scoring six goals in seven matches.

His goal-scoring feats proved instrumental in the Croatians winning the bronze medal in their debut World Cup.

Croatia did not lose a single match in which Šuker scored prior to their semi-final loss to eventual champions France.

Under his highly controversial leadership as the president of Croatian Football Federation,[6] Croatia reached runner-up at the 2018 FIFA World Cup, the nation's highest achievement since their third-place finish.

Along with Raúl and Predrag Mijatović, he formed a dangerous trio that struck fear in the opposing defenses to assure eventual acclaim for the club.

Within the 1998–99 season, his presence at Real Madrid was reduced despite the fact he performed well at that summer's World Cup.

[7] His decision to leave also marked the close of his eight-season-long spell in the Spanish Primera, where he scored 114 goals in 239 total appearances.

He made his league debut on 22 August 1999 in a 2–1 defeat to Manchester United at Highbury, coming on as a substitute for the final 15 minutes.

He played another two matches as a substitute before making his first start in Arsenal's 3–1 home victory over Aston Villa, where he scored a brace, his first two goals in the Premier League.

At 1860 Munich, Šuker made his Bundesliga debut, playing all 90 minutes in the club's 1–0 home victory over Energie Cottbus on 1 December 2001.

In 1990, Šuker was named to the Yugoslavia national team's 22-man squad for the 1990 FIFA World Cup finals in Italy.

[18] On 22 December 1990, Šuker made his debut for the newly established Croatia national team in a friendly against Romania.

He then led Croatia to their first major international tournament, UEFA Euro 1996, with a then-record 12 goals in 10 matches during the qualifying stages.

It was in this match he set up the final score with an unforgettable looping shot over Danish goalkeeper Peter Schmeichel, still remembered as one of the greatest goals in UEFA European Championship history.

In the quarter-finals against Germany, Šuker was fouled by Christian Wörns who received a straight red card.

Lilian Thuram took the match back for the hosts with his only two international goals to give France a 2–1 victory and a place in the final.

Šuker won the Golden Boot as the tournament's top scorer, as well as the Silver Ball as the World Cup's second-best player, behind Ronaldo of Brazil.

Šuker was though noted in endeavouring to keep Croatia's hopes alive when he scored a 94th-minute winner against the Republic of Ireland at Maksimir Stadium in Zagreb.

Šuker was also part of the Croatian team at the 2002 World Cup finals in South Korea and Japan.

Šuker won a total of 70 international FIFA-recognised caps during his senior career, 2 for Yugoslavia and 68[a] for Croatia.

[9] In 1996, in the company of two well-known criminals, Šuker posed for a picture at the grave of Croatian fascist dictator and genocide perpetrator, Poglavnik Ante Pavelić.