Jasikevičius moved to the United States at a young age, playing high school basketball at Solanco High School in Quarryville, Pennsylvania and college basketball at the University of Maryland. Although he was moderately successful on that level, he went undrafted in the 1998 NBA Draft and returned to Lithuania to play for Lietuvos Rytas for one season (1998-99). He spent 1999-2000 in Slovenia with Olimpija Ljubljana.
Jasikevičius won a bronze medal for Lithuania in the 2000 Summer Olympics, when his team lost to the United States by just two points in the semifinals. The margin was the closest at the time since the US started to use professionals, as Jasikevičius' last-second desperation three-pointer that could have won the game for Lithuania had no chance.
Sarunas Jasikevičius moved to Spain and FC Barcelona, playing there from 2000 to 2003. He blossomed into one of the best players in Europe, winning the 2003 Euroleague. That same year, he led Lithuania to the European Basketball Championship, being named MVP in the process. Jasikevičius then moved to Israel's Maccabi Tel Aviv, and promptly won the 2004 and 2005 Euroleague championship with them.
In the 2004 Summer Olympics, Jasikevičius had an amazing performance against the United States, hitting seven three-pointers and scoring 28 points, leading Lithuania to a terrific win. Unfortunately, Lithuania couldn't repeat its triumph, losing to the US in the bronze medal game.
After having great success in Europe, Jasikevičius finally decided to try his luck in the NBA, signing a three-year deal worth $12 million with the Indiana Pacers in July 2005. He will be joining fellow Kaunas natives Žydrūnas Ilgauskas and Linas Kleiza in the NBA.
Šarūnas also has a younger brother, Vytenis, who is currently playing high school basketball at Pace Academy in Atlanta.