The rules set out in the Montreal Convention.
Baggage delayed or lost
When your baggage does not arrive on the conveyor belt you need to fill in a property irregularity report (PIR) on spot.
For the time you are without your luggage you have the right to buy necessary items such as toiletries and some clothes, and get the costs refunded by the airline. Make sure you keep all the receipts and be aware that you have the obligation to keep costs low (luxury goods will not be paid for by an airline).
You have to contact the air carrier in writing and demand the cost refund within 21 days after receiving your luggage.
In case some baggage has not been found for more than 21 days, it is considered lost. A payment of damages in the amount of the current value of the piece of luggage and the items in it can be asked for.
Also in the event of noticing your luggage has been damaged you should fill in a PIR. Within 7 days you have the right to claim damages from the airline (in writing).
For all of the 3 types of baggage mishandling there is a maximum liability for damages of 1131 SDR (special drawing rights) which in general applies. These days 1131 SDR are about € 1.300.
Be sure to check the airline’s terms and conditions regarding hand luggage rules: how many pieces, which size, what items shall not be checked-in but transported in your hand luggage (e.g. money, keys, jewellery, medicines, camera, laptop).
If you still pack these things into your checked-in baggage, costs occurred by a delay in delivery or a loss of the luggage are very difficult to get refunded.