The 30-day rule: the deadline most owners miss
Your window opens when the township list is published, not when the notice reaches you.
Illinois boards of review generally accept appeals for 30 days after the township's assessment list is published in a newspaper of general circulation. That publication date — not the postmark on your notice, not the day you opened it — starts the clock.
Why people miss it
Notices arrive at different times. Some owners get theirs a week after publication, some later, some not at all if an address is stale. The deadline does not move to accommodate any of that.
What to do the day your notice arrives
Call the county Board of Review or check its website for the filing deadline for your township. Write it down. Then decide whether to appeal with time left to gather evidence, rather than discovering on day 29 that you need comparable sales.
If you have already missed it
You generally cannot appeal that year's assessment to the board. Three things are still worth doing: ask the assessor to correct any factual error in your record (that is not an appeal and is not bound by the window), check your exemptions, and prepare now for next year — a uniformity case built in September is far better than one built in a panic.
Certificates of error
Some counties allow a certificate of error for genuine factual mistakes discovered outside the appeal window — a building that does not exist, a square footage plainly wrong. Ask. It is not available for "I think my value is too high", but it is the route for "you are taxing a garage I demolished".