Nearly all mobile phones from around the world will also work here. The only exception might be older phones from outside Europe that aren't dual band. Is your home provider based in the EU? If so, congratulations - no roaming charges as of June 2017. Otherwise watch out for potentially hefty fees.
You can avoid the roaming question entirely by getting a local Estonian number. Alternatively, if you have an Estonian address, you can sign a contract with one of the network providers. See providers' websites for further information, SMS prices, web browsing, etc.: Elisa, Telia, DIIL, Tele2