For Verizon you can set up an internet account and then follow these links My Verizon > my services > Verizon safeguards > spam controls > input phone numbers. This will allow you to block text messages or emails just choose what you want to do. I'm new to bb devices but as far as I know you can't do it on the device.
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Keep in mind dthat block initated from the link above are only good for 90 days and can be renewed. If you elect to purchase usage controls, then they are permenant. This feature is 4.99 per month and has many other controls, mainly for contolling a device whn children are involved.