We were robbed in Barcelona. How is not the topic of this post, but rather the aftermath.
We lost credit cards from three companies: American Express, Chase and Capital One.
Capital One is the company whose card we generally use most, and we've always been happy with them. However, they were least helpful. They would only send replacement cards to our current official address, which is in the US. We are traveling in Europe. Our mail is being forwarded to an assistant, who handles stuff for us while we're away, but by the time she receives the Capital One replacement cards when they are forwarded, we should be near the end of our trip.
Chase was most helpful. They sent replacement cards to our next address in Europe, and in five days the new cards arrived. They sent them through UPS, which delivered on time. It took five days because a weekend and a national holiday held up the process.
American Express was also very helpful. They sent replacement cards to our next address in Europe, but on the fifth day their new cards did not arrive. This appears to be the fault of DHL, which they used to send the cards. We needed to leave the hotel where the cards were mailed to and asked American Express to either chase down the cards and re-send them to our home address or have those cards destroyed and new ones sent to our home address so they'll be waiting when we get home.
Big lesson: don't rely on only one credit card company. And a company may be really great in one respect and not so great in others when it really counts.
(In case you're wondering, we'd had passports and a debit card in a money belt, so we were able to limp on after being robbed. We don't normally charge things on our debit card but did until the new Chase card arrived.)