Taking your smartphone (iPhone or Android) abroad & never even make a call but switch your phone on, the phone can use data using Assisted-GPS or Apps services.
This happens without you realising so it is important that you know whether your phone is making a data connection. It is often worth getting an app to disconnect your data services whilst you are away.
If your smartphone is unlocked, the best way to avoid the roaming charges is to buy a prepaid SIM card from the country your are visiting. These can normally be bought easily and often don’t need any ID to buy in foreign countries.
If it is not unlocked you are limited in your choices. There are some Travel SIMs you can buy that make it cheaper to send & receive calls & texts in foreign countries.