Today is the day players can file for arbitration, and players and teams can exchange numbers on January 19. If there hasn't been an agreement made by February 1, the case goes before a panel of arbiters (arbitrators?)
Here'san excellent explanation of arbitration from MLB.com.
One interesting stat from the article:
What few envisioned was what happened last year, when the 111 players eligible for salary arbitration (eligibility now begins after three years of service) set a new record by receiving an average pay increase of 172 percent.