Once you've checked your luggage prior to travelling, the airline you're flying with and their baggage handling firm are responsible for it. As a result, if you discover that your luggage has not arrived at its destination, they should be your first port of call.
Once you've checked-in baggage claim, you'll see that your luggage is gone. We've all experienced the terrible sensation of being the last person at the luggage conveyor, watching a single crumbled cardboard box go around and around. The luggage handling firms are conveniently positioned in the baggage claim area.