Credit Card Fraud

I received a phone call early this morning with an inquiry from one of my credit card companies about whether I had made a purchase yesterday at a certain location. Not only did I not recall making that purchase, much less at that location, I couldn't have made the purchase since it was for something related to a Dell computer and anyone who knows me knows I only use Mac computers. I called the fraud division of the credit card company and confirmed this was a stolen number [I actually had the card in my possession] and the purchases were not mine. We closed the account, but now I am curious about how someone used my credit card number to purchase items without having the actual card [thus missing the 3 digit verification number on the opposite side]. I hope they catch the thief.