Use of mobile communication in Ukraine has been covered very well in Ukraine forum. Here is some more information on this subject. It applicable mostly to USA travelers, although others may find it useful as well.

 

If you have a smartphone and your mobile provider is T-Mobile USA, call customer service and enable Wi-Fi calling. They may try to charge you for this service, however if you insist, they will eventually give it to you for free.

What that service does: it allows placing and receiving phone calls using Wi-Fi network instead of your provider's mobile/data network. Basically it allows you to connect to T-Mobile web server, which will place or receive calls for you as you were on normal domestic USA network.

Once this service is enabled, try it home BEFORE you leave abroad to make sure it works and your number is registered with the provider, your sound quality will depend on your connection and signal strength, most users rate it between fair and good. Before you leave, set your call options to Wi-Fi only (this is very important to avoid insane roaming charges).

Once arrived to your destination, you should be able to place and receive phone calls using your own number just like home. Obviously this service has its own limitations, and available when you are connected to public or secured Wi-Fi only, also calling a number in Ukraine is the same as calling international number from the USA, so one would use it to keep in touch with family, friends or work in the USA. You should not have problems finding Wi-Fi in any major city in Ukraine.

Another nice thing about Wi-Fi calling: if you have a limited number of minutes in your plan, Wi-Fi calling DOES NOT use your minutes. The bottom line is: you can call any USA number for free and anyone can call you just as you were in the USA. It will also include access to your voice mail and texting.