When you block a phone number from calling you or sending you text messages, the sender does not receive notification that you blocked them. The sender can continue to text and call you; you just stop receiving the messages and phone calls.
Some mobile service providers have a system setup to automatically block unwanted text messages, according to the Federal Communications Commission. This system requires you to forward unwanted text messages to the number 7726, which spells out “SPAM” on the alphanumeric keypad. Once forwarded, your provider blocks the number from continuing to send you text messages. Contact your mobile service provider for specific details regarding their options for blocking phone numbers from your mobile device.