How does the police track down someone who has stolen a credit card?

I lost my credit card abut a month ago and put a hold on the card about 2 days later, but I just got my monthly statement and there were some charges on the card such as gas from a gas station, some fast food restraunts, etc. Is there any way police or whoever can track down the person who did these transactions so I can turn them in? How does that all work?