In California the majority of Driving Under the Influence cases are prosecuted as misdemeanors. This means that upon the successful completion of probation (anywhere from 3-5 years), you may be eligible for an “Expungement,” where a conviction is vacated and a dismissal is entered into the records. If you were convicted of a felony DUI, you must, at the conclusion of your probation, petition the court to lower the felony to a misdemeanor first. Once expunged, you will no longer have a “conviction” on your criminal record (although your DMV driving record may still reveal a “prior” DUI and / or an adverse ruling in a DMV Hearing for purposes of insurance).
Normally a person is eligible to have a misdemeanor DUI expunged when they have successfully completed probation (3-5 years) and the terms of probation (ie. alcohol program, fines..etc.), with no other criminal case(s) pending. However, each city / county has its own standards, so be sure to contact a lawyer familiar with the court where you were convicted in.