Roaming is a communication service of your mobile operator provided in another country. Of course, it is very convenient that you can use your permanent number even when you are abroad. But roaming services are very expensive and often incoming calls are more expensive than outgoing calls. As a rule, Internet roaming is even more expensive and can reach up to 15 dollars per megabyte. Sure, some mobile providers hold special promotions to reduce prices and roaming tariffs but this service must be activated separately. The general rule is: going abroad check your provider for roaming rates in the country of destination as well as about promotions and discounts.
Considering this we would recommend using the roaming services carefully and if you are not sure it is better to turn off mobile internet when traveling because the phone can download updates without your knowledge.
In the settings of smartphones and tablets you can find the set do not use the Internet when roaming. Better yet, turn off mobile data transfer.