I described the Republican primary here; now for the Democrats. There is more of a contest than on the Republican side, but the Democrats have a definite front-runner: State Treasurer Alexi Giannoulias.
Giannoulias, a 33-year old Chicagoan, was elected to his current position in 2006. He has a law degree, has worked as a banker, and briefly played professional basketball in Europe.
Giannoulias was mentioned as a possible appointee to the Senate seat, when Barack Obama resigned from the Senate after being elected president. I presume Giannoulias would not have accepted an appointment from then-Governor Rod Blagojevich, after the governor was arrested in connection with accusations of corruption regarding, among other matters, the Senate appointment. The conventional wisdom was that only someone whose political career was largely behind him, such as Roland Burris, would have taken the risk of accepting an appointment from Blagojevich. Burris currently holds the Senate seat on an interim basis, and is not running in this year's election.
Here is a Rasmussen poll, showing Giannoulias in the lead in the primary, with 31%.
In second place, with 23%, is David Hoffman, 42, who is inspector general in the city government of Chicago.
The third place candidate, with 13% support in the poll, is Cheryle Jackson. She is president of the Chicago Urban League, and was an aide to Blagojevich.