I took British Air last April from San Francisco to Rome. I was going to be in Italy for several weeks in a variety of locations, including some events for which I needed dressy clothes. So I had a large bag which I checked. On arrival in Rome, Passport control took a very long time, even though I had flown Business Class (with miles) and got off the plane quickly. By the time I reached the BA carousel, at the very end of an approximately 1000 foot long baggage claim concourse, only 2 or three bags were on the carousel, not including mine. I reported the lost bag at the carousel agent for BA's office, was given a claim number, and a phone number, and told I would receive the bag soon. I was also given a website on which to monitor by bag and to update my address as I was traveling.
Long story short, after no bag showed up in a couple of days, BA told me to purchase enough clothes to finish my trip, and I would be reimbursed. I had one afternoon in Rome to do this, so purchased the bare minimum. BA was nearly impossible to reach. My calls usually, if answered at all, resulted after a long wait time in a message to call back.
On my way back to the states, I went through Heathrow, and spoke with the BA Lost Baggage attendants there. The head guy looked up my claim, and informed me that BA had removed my luggage after 12 times around the carousel, as was their policy, and it was in Rome. I eventually filed a claim as I was never contacted by BA. This involved a massive amount of documentation of purchased before and during the trip. They denied it, saying that once my bag was on the carousel, they had no responsibility, per international law. They referred me to an arbitration group, working for the airlines in Britain, who eventually came to the same conclusion, denying any claim.