Most noncitizens in the US must tell USCIS their new address within 10 days of moving. This includes green card holders, visa holders, refugees and asylees. (Diplomats and some officials are not included.) It is free.
Open uscis.gov/addresschange.
Sign in with your USCIS online account, or create one. See USCIS case status, online account and notices.
Enter the new address. If you have pending cases, add each receipt number so every case moves with you.
Save the confirmation page or email. That is your proof.
You can also file a paper Form AR-11, but online is faster and updates pending cases.
If you have a case in immigration court
USCIS is not the court. You must also file the court's own change-of-address form (EOIR-33) with the immigration court within 5 days. Your lawyer can help.
F-1, J-1, M-1 students: your DSO or RO within 10 days. They update SEVIS.
OPT and STEM OPT students: update in the SEVP Portal within 10 days.
H-1B and other workers: your employer, especially if your work location changes. A new work site can need new paperwork before you start there.
Social Security: update at ssa.gov.
IRS: your next tax return updates it, or use Form 8822.
DMV: most states require an update within a few days or weeks. This differs by state; see In your state below.
USPS: mail forwarding at usps.com.
Changing the address with the post office only. USCIS does not get it.
Updating the profile but not the pending cases.
Waiting until a card is lost in the mail.
Students forgetting the DSO. Your SEVIS address must be current.