Changing, Replacing, and Renewing Your Driver’s License — California Permit Test Rules (Section 4)

Address changes

After you move, you have 10 days to tell DMV your new address.
You can report a change of address to DMV either online or by mail.
Making sure DMV has your current mailing address on file is your own responsibility.
Reporting a new address does not mean DMV automatically sends you a new license. You can ask for a replacement license, but there is a fee.

Driving with an expired driver's license is illegal.
A license that is lost, stolen, or damaged can be replaced through DMV, and a license can also be renewed there.
If you are not eligible to renew your license online, you have to go to a DMV office.
DMV may ask you for extra proof of identity before it will issue you a driver's license.
Your driver's license can expire on the same date as your identity document. In that case, you must show a valid identity document.

As soon as you get a replacement license card, your old card stops being valid.
If you later find your old license card after getting a replacement, you should destroy it.

You must send your extension request before your driver's license expires.
You cannot get the one-year out-of-state extension on a limited-term driver's license.
If you're outside California and can't renew your driver's license, you may request that it be extended for one year (limited-term licenses don't qualify).
Before your license expires, email DMV at dl-extensions@dmv.ca.gov with your name, license number, date of birth, California home address, and the address where you're staying out of state.

Restated from the California Driver's Handbook, Section 4. Read the official text.