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(Keep in mind that the layout of the website may have changed since this writing, so feel free to update this page as needed.)  AT&T:  1.  First report your spam text messages.  Do this by forwarding the message to short code 7726 (spells 'SPAM').  The system may ask you to report the phone number that spammed you.  Verizon Wireless: Head on over to http://www.verizonwireless.com, and make sure you're logged in first, if not, log in. Under "My Verizon" you should see "My Services", and then under My Services, you should see a list of options, at the bottom of the list should be "Spam Control". Go ahead and click that, and from there you can block up to five numbers and 15 internet emails/domains/etc.  T-Mobile: Log into http://www.t-mobile.com and go to "My t-mobile" using the t-mobile sites drop down at the top of the page. Now, search for "Change plan or services" and click the link. You will be taken to a page with the section "Your Current Services" where you'll have to click the "change services" button. Here, you can block text messages, instant messages, photo messages, messages sent via e-mail, or even all text messages.  Sprint: Log in at http://www.sprint.com. On the top navigation bar, move the mouse to hover over "Digital Lounge", then click "Messaging" on the smaller menu that appears. (Alternately, click on "My device & media" and then click on the "Messaging" icon.) Click on the "Block Texts" button under the "Texting" section. Select the "Block messages from all senders in my block list" option. In the text box, enter a phone number, email address or domain (such as Comcast.net) that you want to block.  Click the "Add" button.  Click the "Save changes" button.  Virgin Mobile: Check the Messaging Settings page on Virgin Mobile's website (http://www.virginmobile.com) to block text messages from up to ten telephone numbers or email addresses; you can also change preferences on your handset (VirginXL or VirginXtras > Messaging > Messaging Management).

Summary:
In addition to calling your carrier to add these settings, you may also be able to  block spam through the carrier website as follows.