Each country has its own cell phone network and these might be different from other countries as well. While some of the smartphones like iPhones are made for global networks, some are made for specific networks in some countries. So if you are a frequent traveller, you might be using different networks in multiple countries. Before you go to a different carrier or country, it is advisable to check if your phone is compatible with the network.
Will My Phone Work is a useful website which shows the compatibility of your smartphone for different countries and network.
The website has 8750 mobile phones listed along with 837 carrier networks. All you need to do is select a mobile device (cellphone, smartphone, or tablet) from the drop-down lists below. Then, choose a mobile carrier network that you would like to use the device on.
When performing a search, you will be presented with three networks: 2G, 3G, and 4G LTE. A check mark means that the device is compatible on that network and will work. A red X means that the device is not compatible on that network and will not work. You can choose the brand, model, sub model (varies in diff countries), country and the carrier.
The website has a comprehensive list of smartphones and carriers in almost all countries and pretty useful to find out the network compatibility for any smartphone.
The website has list of almost all iOS, Android and Windows Phone devices to choose from. If you are a frequent traveller, this website should be in your bookmarks.