I've had my credit card stolen three times over the years, in various scenarios (out of the mail, out of my jacket, and directly out of my wallet when it was unattended for a moment whilst I was in the pisser).
In each case, the credit card company eliminated the charges. In one instance, they called me first to say they had noticed unusual stuff. That's the good news... no effect on me except a hassle.
What bugged me is that they make ZERO effort to catch the perps! Incredibly, in one case, the perp(s) used the card to release a vehicle that was impounded by a towing company, filled up the car with gas, and then the card was seized by a clerk at the next shop after I had reported it stolen. You'd think all that would give the credit card company and law enforcement enough information to act upon. But no. They don't care or bother about catching people. They just reimburse you for the charges, and make it up on the interest rate to others.
I dumped all my credit cards years ago. Why bother? Just a bank card. A lot of banks will also put your photo on a card if you ask, which stops a lot of theft except for card-swiping at gas stations and whatnot.