If you're relying on Wi-Fi, it's important that you turn off cellular data on your phone, otherwise you may inadvertently rack up international roaming charges. Skype, Google Hangouts and other apps also let you make free video calls with other users over an internet connection.
Airplane mode turns off all your phone's radio connections (cellular, Bluetooth, and Wi-Fi), but apps that don't require an internet connection will continue to use data. Your best bet to avoid expensive roaming charges is to turn off data roaming or — even better — use a prepaid data plan.
Check your Cellular Data options and turn off Data Roaming. In the Settings app, tap Cellular, or Cellular Data, or Mobile Data. Turn on Cellular Data, then tap Cellular Data Options. Turn off Data Roaming.