Yes, landlords will call a tenant's references (previous landlords) to verify rental history as part of their tenant screening process. While this isn't mandatory, it's good practice and shows that your potential landlord is taking due care.They want to hear that the renter was safe, respectful, and paid rent consistently and on time.
If you don't have a rental history, then there are other ways you are able to demonstrate your trustworthiness by providing enough financial and employment documents for the landlord.
Pro tip: use your liv.rent renter's resume to hold, store, and organize your references. That way, they're always available to you when you're ready to apply for a rental.