An earth-boring tool includes a cutting element comprising a hard material and at least one of a signal generator configured to provide an electromagnetic or acoustic signal to an interface between a surface of the hard material and a surface of a subterranean formation, and a sensor configured to receive an electromagnetic or acoustic signal from the interface. A method of forming a wellbore includes rotating the earth-boring tool within a wellbore and cutting formation material with a cutting element, transmitting a signal through the cutting element to an interface between the cutting element and the formation material, and measuring a response received at a sensor. A cutting element includes a transmitter oriented and configured to dispense a signal to an interface between the cutting surface and a surface of a formation and a sensor oriented and configured to measure a signal from the interface.