Standard information theory deals with alphabets and their transmission over communication channels. Here we examine the novel features introduced by allowing the alphabet symbols to be quantum states. A simple device for communication of one bit of information is discussed and the transition between quantum and classical behaviour is highlighted. A further level of complexity is introduced when we allow the communication to take place with quantum-correlated states. We show, by the simple expedient of constructing a suitable local hidden variable theory, that many of the novel features of such communication are compatible with the concept of local realism. We introduce a convenient parameter for characterizing the contribution of the quantum entanglement to the communication.