By 1 July, new rules will come into force in the European Union which will cap bills for downloading data.
But, until then, people travelling in Europe could face unlimited bills.
And anyone visiting non-EU countries, like Turkey, the US or the Caribbean, will continue to have no limits on their internet usage.
If you use your phone in the UK to connect to the internet, for example to check emails or go on Facebook, you don’t usually need to worry about the bill – most home tariffs include unlimited downloads.
But, if you take a smartphone, like an iPhone, on your travels, it can have expensive consequences.
One German man was reported to have been charged £41,000 after downloading a television programme onto his phone.