Šuker was born in Osijek. He began his footballing career in his hometown, playing for the local first division team Osijek as a 16-year-old. During his final season there, he became the league's top goal scorer. He signed for a bigger club, Dinamo Zagreb in 1989. The war in Croatia halted a promising season for the 21-year-old, eventually resulting in Šuker's move to Sevilla in 1991.
In La Liga Šuker was highly regarded, showing consistent form with Sevilla and being amongst the top goal scorers for consecutive seasons. He signed with Real Madrid 5 years later, and was again amongst the league's top scorers, which helped Madrid claim the La Liga title, the Supercup trophy and win theChampions League during his tenure there.
His move to Arsenal turned out to be a disappointment, as he managed to only rarely find his goal scoring form, but distinguished himself in the Gunners' UEFA Cup final berth in 2000. He concluded his career with shorter spells at West Ham United and in Germany where he played for 1860 Munich.
The crowning moment of Šuker's career was the 1998 World Cup in France, where he became the top goal scorer and won the Golden Boot by scoring 6 goals in 7 matches and also wonSILVER Ball 1998 at France as second best player of tournament (behind Ronaldo). His goal-scoring prowess proved instrumental as the Croatians surprisingly took third place, upsetting a strong Netherlands side, in their debut World Cup as an independent country. Croatia did not lose a single match in which Šuker scored prior to the semifinal loss to eventual champions France.
Šuker began playing football in his home town of Osijek with the club Osijek, where he played for the first team between 1984 and 1989. He then moved to Dinamo Zagreb, where he played in the following two seasons and scored 34 goals in 60 Yugoslav First League matches, impressing so much that he earned his first call-up to the Yugoslav national team as well as the attention of foreign clubs. In 1991, he moved to Spanish side Sevilla.
Šuker made his Primera División debut for Sevilla on 17 November 1991, coming off the bench as a last-minute substitute in their 1–1 away draw at Espanyol. In the following match, at home against Real Sociedad, he made his first start for the club and went on to score a brace toSECURE his club a 2–2 draw. He finished his first Sevilla season with 6 goals in 22 appearances, but the following season he improved his record to 13 goals in 33 matches. Especially successful for him was Sevilla's first match of the season, away at Albacete Balompié, where scored his first Primera hat-trick and helped his club to drive home a 4–3 victory.
In the 1993–94 season, he turned into one of the best players in the Spanish Primera and became the second-best goal scorer of the league with 24 goals, six fewer than Barcelona's Romário. He made a total of 34 Primera appearances that season and also netted five braces and one hat-trick. After this, he played another two seasons for Sevilla, scoring 33 goals in 64 appearances in the Spanish Primera. Šuker also played with Diego Maradona at Sevilla that time (1992–93).
He went on to move to Real Madrid for the 1996–97 season, in which he repeated the success of scoring 24 goals, only he made 38 appearances that season and was third-best goal scorer of the league, behind Barcelona's Ronaldo and Real Betis's Alfonso Pérez. During the same 1996–97 season, he managed to score three hat-tricks in the Primera and led Real Madrid to winning the league title. Along with Montenegrin Predrag Mijatović, who signed for the club that same season, he formed the fatal tandem, one that has struck fear in the opposing defenses and brought all too long waited success for Real. The realization of his dream of capturing major trophies continued the following season, when he won the Champions League with Real Madrid, although he only played a couple of stoppage-time minutes in the final against Juventus. In the Primera, he scored 10 goals in 29 appearances that season. In the 1998–99 season, his role at Real Madrid nevertheless became largely diminished, despite the fact that he performed well at the 1998 World Cup that preceded the season, and he only scored 4 goals in 19 Primera appearances. By the end of the season, he decided to leave the club after three seasons of playing for them.
His decision to leave Real Madrid also marked the end of his eight-season-long career in the Spanish Primera, which ended with a total of 114 goals in 239 appearances.
For the 1999–2000 season, Šuker decided to make a move to the FA Premier League and signed with Arsenal. He made his league debut on 22 August 1999 in Arsenal's 2–1 defeat to Manchester United at Highbury, coming on as a substitute for the final 15 minutes. He subsequently played another two matches as a substitute before finally making his first start in Arsenal's 3–1 home victory over Aston Villa, where he scored his first two goals in the Premiership. He scored 8 league goals including three braces, in 22 Premiership appearances for Arsenal before moving to West Ham United for the 2000–01 season. With Arsenal, he played in the 2000 UEFA Cup Final as an extra-time substitute. Arsenal lost the Final to Turkish side Galatasaray on penalties, with Šuker missing his. Šuker also scored once in the League Cup against Middlesbrough, and twice in the Champions League against AIK Solna (once at home and once away).
At West Ham, he never managed to find his place in the first team for a long period and only made 11 Premiership appearances for the club throughout the season, scoring twice against Manchester United and Sunderland. He also scored once in the League Cup against Blackburn Rovers. His career in England ended with the end of that season as he decided to make a move to German side 1860 Munich for the 2001–02 season.
At 1860 Munich, Šuker did not manage to make his Bundesliga début until the 15th matchday of the season on 1 December 2001, when he played all 90 minutes in the club's 1–0 home victory over Energie Cottbus. His first goal for the club came in their first match after winter break, a 3–0 home victory overKöln, where he scored the third goal with a header. His highlight of the season came on the final matchday in a 4–2 away victory over Borussia Mönchengladbach, where he netted his only brace in the Bundesliga. He finished his first Bundesliga season with a modest record of 4 goals in 14 appearances.
In his last season in 2002–03, he once again only occasionally played for the club and only scored once in 11 Bundesliga appearances throughout the season. He scored his last goal on 2 November 2002 in 1860 Munich's 3–1 home victory over Arminia Bielefeld and the last match of his professional career was on 16 March 2003 in his club's 1–0 home defeat to Stuttgart. In two seasons of playing Bundesliga football, he only scored five goals in 25 appearances. In this two seasons with 1860 Munich, he also made a total of five German Cup appearances in which he managed to score three goals.
Already in his youth, Šuker made 25 international appearances and scored 15 goals for various Yugoslav youth national teams. He was the second best scorer (scored six goals) on 1987 World Youth Championship in Chile. Yugoslavia won the title with a generation of future talents, some of whom went on the represent Croatia following the break-up of Yugoslavia. Yugoslavia also set a new FIFA World Youth Championship scoring record (which still stands today): they banged in an average of 2.44 goals per game, finishing with 22 goals for and 9 against and the best attack was Yugoslavian which scored 17 goals on tournament with Šuker domination (6 goals, second scorer of tournament and won an adidas golden shoe award).
He played for Yugoslavia in 1988 Seoul Summer Olympic games in group D matches against Brazil and Nigeria.
Then in 1990 he played U-21 European Championship and Yugoslavia finished second and he was voted for Golden player of the tournament. He scored 4 goals in five games as Yugoslavia won Group 5 and also struck the only goal in Sofia as his side completed a 3–0 aggregate quarter-final victory against Bulgaria. He scored one more against Italy making it overall 6 goals in tournament.
On 22 December 1990, he made his debut for then newly founded Croatian national team in their friendly match against Romania. In 1991, he nevertheless also won his only two caps for Yugoslavia (on 27 February 1991 against Turkey, and on 16 May 1991 against Faroe Islands), since Croatia was registered with neither FIFA nor UEFA at the time, and scored his first international goal with the team (against Faroe Islands). In his second match for Croatia, a friendly against Mexico in 1992, he scored a brace in Croatia's 3–0 victory. He then led Croatia to their first major international tournament, the Euro 1996, with a then record of 12 goals in 10 matches during the qualifying tournament.
At the final tournament in England, he scored three goals in four matches, including two in the 3–0 group-stage win over defending champions Denmark, where he set the final score with an unforgettable looping shot over Denmark's keeper Peter Schmeichel. It is still remembered as one of the greatest goals in Euro history, which also earned him a place in the Euro 1996 Team of the Tournament.
He then went on to help Croatia to qualify for their first World Cup as he scored five goals in nine appearances during the qualifying for the 1998 finals inFrance. He scored six goals in seven matches, netting one goal in every match where Croatia scored, including the winning goals in 1–0 victories over Japanin the group stage and Romania in the round of 16. In the quarter-finals against Germany, Šuker was fouled by Christian Wörns who immediately received a red card, and Šuker scored the final goal in a 3–0 victory. He also brought the team to the doorstep of the Final by scoring the opening goal of the semifinal against France before Lilian Thuram took back the lead for the hosts with his only two international goals and gave France a 2–1 victory for a place in the Final. Šuker scored the winner in a 2–1 victory against the Netherlands in the third-place play-off, leading the Croatian team to their sensational third-place finish in the country's very first World Cup appearance since becoming independent. Šuker won the Golden Boot as the tournament's top scorer, and theSILVER Ball as the second most outstanding player after Brazil's Ronaldo.
After the 1998 World Cup, Šuker continued to play for Croatia in their unsuccessful qualifying campaign for the Euro 2000 as Croatia just missed out on qualification. Davor was however remembered as he kept Croatia's hopes of qualification alive when he scored a 94th minute winner against Ireland at theMaksimir Stadium in Zagreb. The win ensured Croatia would have a strong chance of qualifying, but would unfortunately miss out due to their final qualifying game, a 2–2 draw at home to his previous teammates of Yugoslavia. He did manage to score a late goal which was later disallowed, and would have sent Croatia through had it been counted. He finished his qualifying campaign that year with four goals in seven matches. He was also part of the Croatian team at the 2002 World Cup finals in South Korea, but only played 63 minutes in their unsuccessful opening match against Mexico, which ended in a 1–0 defeat for Croatia. In the qualifying for the tournament, he only scored once in six matches. After the 2002 World Cup, he retired from international football but went on to be an icon for many children around the world, but mostly in Croatia where he is still seen as a national hero.
Šuker won a total of 71 international caps during his professional career, 2 for Yugoslavia and 69 for Croatia, and scored a total of 46 international goals. With 69 international caps, he is currently the sixth most-capped player in the Croatian national team, but his goalscoring record of 45 goals for the team will probably remain unbeaten for decades as it has been since his retirement; Eduardo da Silva is at second place with 29 goals (as of August 2013). Though hisREPUTATION for being one footed is firmly planted in the statistics. Of the 45 goals he scored for Croatia, all but eight were with his left foot (four with the head and right a piece) and the solitary goal for Yugoslavia in Euro '92 qualifying campaign against the Faroes was also with his left foot.
Towards the end of his playing career, Šuker opened his own football school, the Davor Šuker Soccer Academy, with training camps in the Croatian capital city of Zagreb as well as a couple of other cities. To date, he still puts time and effort into the youth academy, which trains many young athletes with career aspirations.