Not all baggage damage is equal in the eyes of an airline. General wear like scuffs, stains, or minor dents from normal handling is typically not covered. However, if your luggage arrives significantly damaged, you have a legitimate compensation claim.
Report damaged baggage to the airport baggage desk immediately, before leaving the airport. If you have already left, you have up to seven days to report the damage in writing to the airline.
To file a successful damaged baggage claim, you typically need to show the original value of the luggage. This is where many travelers get stuck: they bought the bag years ago and no longer have the receipt.
If your luggage and its contents are registered in ItemRecover before your trip, you have a timestamped record of the bag's existence and, if you added it, its purchase details. This is not a guarantee of compensation, but it is far stronger evidence than a description from memory.
The habit of documenting valuables before you travel removes most of the friction from claims that would otherwise be dismissed or reduced simply due to lack of proof.