The four main network providers in Italy are Vodafone, Tim, Tre and Wind. Almost all phones should work in Italy. Just check to see if your mobile phone supports GSM 900 and GSM 1800 frequencies.
If travelling from outside the EU, it is worth making sure you have an international call package with your mobile phone provider before visiting Italy. And make sure that data roaming is switched off to avoid an expensive bill when you get back home. However, the other option is to buy an Italian SIM card to call any numbers in Italy during your stay. Just make sure that your phone is unlocked and walk into any cell phone shop with some form of identification and ask for a prepaid SIM card. Cards can cost as little as 5 euros which gives you 5 euros worth of calls, texts and data. If during your stay you need to top up your credit, just visit any tabaccaio or supermarket. Ask for a ‘ricarica’, tell the shopkeeper who the mobile phone provider is and how much money you would like to top up with.
If travelling from inside the EU, data roaming fees are capped.
Italians also use WhatsApp frequently rendering SMS messages almost obsolete. Leaving recorded WhatsApp messages is also extremely common.