There are all sorts of scams that don't require a computer to do. For example, with a little bit of work on the computer, I can find out your name, phone number, address, and what types of credit cards you have. I could then call and say "Hi, I am from Mastercard, I am looking for yourname. We have reports of fraudulent charges on your account". I could ask something that would scare you - like did you order $4,000 worth of video games to be shipped to South Korea". Of course, that is how scams really work. They create fear, so that you go along with them. In this case, the person would promise to clear the fake charges off your account, but only after "verifying" some information. To do so, they'd ask some really obvious information, and then eventually get your credit card information from you.
I read about something that was new to me - a similar scam regarding jury duty. The person wishing to scam you will call and say that a warrant has been issued for your arrest due to you missing jury duty multiple times. They'd ask for information for verification purposes to clear this, and of course when they ask for things like social security number, that is when they are getting the information they want.
The question I get asked when I bring these things up in class is "so how do I know it is real"? If you are not sure - call the company back. If it is a credit card, call the number on the back and get the fraud department on the phone. If it is a jury duty issue, get the county clerk on the line. If someone is calling you about it, then you should be able to call them and get the same information and get it worked out, and I am much more inclined to trust it if I am the one placing the call.
Link to jury duty scam article (fbi.gov)