During his time with the national team, the Czechs made only one World Cup appearance, in 2006. Koller scored the first-ever World Cup goal for the Czech side when he netted in the 5th minute of their opening match against the United States, leading the way to a 3-0 victory. Those were the Czech side's only goals of the tournament, however, and they were eliminated in the group stage after losses to Ghana (0-2) and Italy (0-2).
Koller has a well-traveled career, having played club football in the Czech Republic (with Sparta Prague), Belgium (with Lokeren and Anderlecht), Germany (with Borussia Dortmund and Nuremberg), France (with Monaco), and Russia, where he currently plays for Krylia Sovetov Samara.
His longest club tenure to date was with Borussia Dortmund, where he played from 2001 to 2006, making 137 appearances and scoring 59 goals. He helped them claim the Bundesliga title in the 2001-2002 season.
An imposing physical presence at 2.02 meters, Koller has earned a number of honors throughout his career, including Belgian League top scorer in 1999 and Belgian League Player of the Year in 2000.