In iOS 7, you can (finally!) block phone calls, messages, and FaceTime requests. In the Settings app you can go to Phone > Blocked or Messages > Blocked to add phone numbers and email addresses.

A catch as of iOS 7.0.2, however, is that phone number(s) or email(s) you want to block must already be added to a contact in your device; tapping the Add New button displays a searchable list of all your contacts, and there is no way right now to manually add addresses. I should also note that this is for blocking incoming phone calls, iMessages, and FaceTime requests from phone numbers and email addresses (iMessage allows you to register both for these features); as far as I know, it doesn’t work to block incoming SMS or actual emails.

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Update: Thanks to Brian Webster on ADN, you can block numbers and addresses without having to add them to a contact. Just go to the Recent list in the Phone or FaceTime apps, or tap ‘Contact’ at the top of a conversation in Messages, then tap the (i) button and scroll to the bottom of the details for that number or address to find the ‘Block this Caller’ option.
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On the upside, tapping a contact will add all of their phone numbers and email addresses at once, so there’s a trick you can use to save some time when it comes to random addresses not yet assigned to a contact:

  • create a new contact, name it something like “Undesirable”
  • add all unwanted numbers and emails to this new contact
  • whenever you make significant updates to your new contact, re-add them to the Blocked list (no, it doesn’t update automatically)