What do I do about purchases I didn't make?

You do not say where you see this purchase. If it is an e-mail or text message are you sure it is real and not an attempt to steal your private information ('phishing') (very common)?

Phishing & Other Suspicious Emails - https://www.apple.com/legal/more-resources/phishing/

Identifying legitimate emails from the iTunes Store - http://support.apple.com/kb/HT2075 (the previous link is more specific)

Forward attempts to: reportphishing@apple.com

If you still think the charge is real:

See your purchase history in the App Store or iTunes Store [iOS, computer, or web] - Does not list purchases made by others under Family Sharing; those have to be checked from their accounts. http://support.apple.com/HT204088

Also follow the steps in this support document --> If you see ‘itunes.com/bill‘ or an unfamiliar charge on your bank, credit card, or debit statement - https://support.apple.com/HT201382

If neither you nor a family member (if applicable) has a record of this purchase and you only saw it on a statement for a card you alone control, contact your bank or card company about card fraud. Apple does not handle that.

If you do now recognize this purchase and are asking for a refund then realize Apple's terms of purchase for most countries are effectively, "All Transactions are final" (check terms at: https://www.apple.com/legal/internet-services/itunes/us/terms.html ). Apple does refund on a case by case basis, but they can also refuse.

To "Request a refund for apps or content that you bought from Apple", click here → https://support.apple.com/HT204084

Report a Problem - https://reportaproblem.apple.com/?s=6

If a reporting a problem request is unsuccessful you can also try clicking here → https://support.apple.com/choose-country-region/media-services Select your country, then a product.