Here is some useful information in the unfortunate event that the airline you are flying on damages or (even worse) loses your luggage. The first thing to do is to go directly to the airline itself!
For hand luggage in particular, the Montreal Convention states that all the airlines registered in countries where it is enforced are required to compensate the passenger up to 1000 SDR (Special Drawing Rights), equivalent to approximately 1,167 euro, if hand luggage is damaged, destroyed or lost at the end of the flight. The airlines registered in countries that adhere to the Warsaw Convention are required to compensate the passenger up to a maximum of 332 SDR (Special Drawing Rights), approximately 387 euro. For checked (or registered) baggage: community airlines and those registered in countries that adhere to the Montreal Convention must compensate the passenger up to 1000 SDR (Special Drawing Rights) or about 1,167 euro if the baggage is damaged, destroyed or lost at the end of the flight, or if the delay in baggage delivery caused first-rate expenses. The airlines registered in countries that adhere to the Warsaw Convention are required to compensate the passenger with 17 SDR (approximately 20 euro) per kilogram of weight, up to the maximum number of kg accepted for carriage in the hold with no extra fee. The compensation is due only if the airline is liable for the damage. N.B. Baggage weight limits are set by individual airlines and are indicated in the conditions of travel (or General Conditions of Carriage) whose main elements are shown on the airline ticket. It is also possible to file a statement of high value baggage, which must be made in advance, or at check-in at the latest. Any passenger who wishes to declare high value luggage has the right to view a price list that defines any additional costs.
In case your baggage is lost or damaged the most urgent thing to do is to contact the airport lost and found office and state which airline you flew with. It is especially important to keep the tag with the baggage code that you are given at check-in for hold baggage.