The government's top legal adviser has issued a new warning over abusive tweets and Facebook posts.
Attorney General Dominic Grieve said users should be aware of how easy it can be to break the law.
But he said the government didn't need to introduce new laws because existing ones already make it illegal to "grossly offend" or "cause distress".
It comes after 21-year old Liam Stacey was jailed for mocking footballer Fabrice Muamba on Twitter.
Dominic Grieve said: "If somebody goes down to the pub with printed sheets of paper and hands it out, that's no different than if somebody goes and does a tweet.
"The idea that you have immunity because you're an anonymous tweeter is a big mistake.
"If necessary we will take action.
"I don't want to take action but if I think it is necessary to prevent crime, such as racially aggravated harassment, then I won't hesitate to do it."
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Cumbria Chief Constable Stuart Hyde leads the UK policing approach to online crime.
Sarah thinks children should be taught more about social networking
He says they are leading the way internationally when tackling it.
"The warning is this," he said. "We fight for people's rights in order to make free comment.
"But with that comes a responsibility to act within the law".
Mr Hyde also said they could quite easily trace owners of online accounts even if they had been closed.
Sarah, 21, is a student at Pontypridd in south Wales and thinks schools should teach children about the risks.
She said: "You don't really know much about what you can and can't say, so you don't know what's a case you can report and what's not.
"So until you know that, you're not going to report anyone."
In a statement Facebook said: "Facebook is a safe and positive platform for people to share things with the people who matter to them.
"On the rare occasions when people come across content or behaviour which makes them uncomfortable, there are reporting tools on almost every page of the site.
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You may not use our service for any unlawful purposes or in furtherance of illegal activities. Accounts engaging in these behaviours may be investigated for abuse
"We co-operate with the police to the extent required by law to make sure the tiny minority of people intent on causing harm to others are brought to justice."
"Accounts engaging in these behaviours may be investigated for abuse.
"Accounts under investigation may be removed from search for quality. Twitter reserves the right to immediately terminate your account without further notice in the event that, in its judgment, you violate these rules."