And some of you've told Newsround how it happens.
"I was in my bedroom - and I got a text from someone saying they wanted to beat me up for something I didn't really do," said Daniel, 14.
At Daniel's school they get older pupils to mentor anyone who's been threatened on their phone, and try and find out who sent the message.
Text bullying is upsetting
Many of you have also emailed CBBC Newsround Online to tell us how horrible bullying feels.
"I have been bullied by text and e-mails. It is very upsetting," said Kimberly, 12, Berwick.
But several of you have sent in suggestions on how to avoid nasty texts.
"Be careful who you give your number to," said Jimmy, 11, from West Kilbride.