The oldest problem in quantum information theory is how the laws of quantum systems affect our ability to store, transmit, and receive ordinary "classical" information. Theorems by Holevo and by Schumacher and Westmoreland relate the classical information capacity of a quantum channel to properties of the ensemble of signal states, most naturally expressed in terms of the quantum relative entropy. Armed with these results, we can discuss the information-theoretic basis for quantum cryptography, show how to use a quantum channel to send classical information in the most efficient way, and rigorously derive results (previously known as informal "folk theorems") about the thermodynamic cost of communication.