What happens if an airline damages your luggage?

If you arrive in the baggage hall to find your luggage has been damaged, go to the relevant luggage handling counter at the airport and fill in a Property Irregularity Report (PIR). The airline will then contact you to discuss the extent of the damage and its recourse, which could take the form of a new suitcase. It's not a legal requirement to have a PIR, but it does speed up the claims process.