A Card Verification Value code (CVV) is an authentication code found on credit cards. It's usually a three-digit code on the back of a card in the signature field or, in the case of American Express, it's a four-digit code on the front right of the card. A CVV provides a cryptographic check of the information on the card. It's also used to make sure you actually possess the card. If you've lost your card and are waiting for a new one, or if the number has rubbed off the back of your card, you can still use it.
Go through a merchant's checkout and see if they require a CVV. Steer away from larger companies: they almost all now require you to enter a CVV if purchasing online.
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Ask the merchant if it will accept a card without a CVV. It may be able to take your card number, depending on what processor it uses for credit cards. Some processors do not perform a CVV check, and so you may be able to place the order over the phone.
Visit a store in person. If you swipe your card at the register, you don't have to enter the CVV as being there to present the card is proof that the card is in your possession.
If the CVV on your card is illegible, call your card company and ask for a replacement. Make sure customer service knows it isn't a lost card, otherwise it will freeze your account temporarily, and you won't be able to use your card at all.