If your luggage has been damaged during a flight, the responsibility for the damage lies with the airline concerned. At most airports, you can preferably submit the damage report online or directly at the baggage tracing office (Lost and Found at the airport).
After your report, you will receive a written confirmation with a reference number, the so-called PIR number (e.g. FRALH12345). Be sure to keep this number carefully, as it is required for further processing.
If you only notice the damage after arriving home or at your hotel, you must report it within seven days of your flight. This deadline is important to ensure your case is processed quickly and that you do not lose your entitlement to compensation from the airline.
By the way, you can also claim compensation for delayed luggage. If your checked baggage arrives late and you wish to claim reimbursement for necessary toiletries and clothing according to legal regulations, you can usually apply for this online with your airline. The reimbursement helps to cover unavoidable expenses in the meantime.
If your luggage has been damaged, you can also contact your airline to claim reimbursement for the costs incurred.