First, I have accounts and cards from Citibank in the US, and from KBC as well as Citibank in Belgium.
The cards (both banking/debit and credit) from Belgium have chips on them and are inserted into (as opposed to being slid through) a credit card machine.
You validate the card by signing the transaction with a PIN, whereas a US card is validated by a signature.
PIN signing/validation of transactions is more secure and was introduced over ten years ago in Europe.
How many retailer employees validate a signature on a receipt to a signature on the card?
Being able to pay in Europe using a US card is fairly commonplace.
You might need to swipe vs. insert (which might be uncommon for the retailer), you might need a PIN (so ask for it, it's easy to get) or you might need to sign.
It is also dependent on the payment network the retailer is using and you should be prepared with an alternative (cash, local account/card or the like).
I tried to provide a comprehensive answer, but I hope i didn't confuse people any more.
Best,
Andres
Wells Fargo, BofA and JPMC are experimenting with 'smart cards' and are rolling them out in limited numbers in the US.
You can expect to see them more and more over the next year or two, and they will entirely replace signature-based cards in 5-10.