The rapidly rising need for computer communications has been met for the most part by utilization of the ever expanding network of voice-bandwidth channels. Transmission of digital signals over these analog channels involves a modem for modulation and demodulation of a voice-frequency carrier. The usual forms of amplitude, frequency, and phase modulations are described together with their basic characteristics, such as efficiency of bandwidth utilization. The principles of signal shaping and filtering for optimum signal-to-noise performance and minimization of intersymbol interference are discussed. Also covered are methods of synchronization, carrier recovery, effects of channel impairments, and the application of automatic equalization. The choice among modem designs is shown to be influenced by bit speed requirement, permissible error rate, type of channel, receiver startup characteristic, and tradeoff between modem and line costs. The functions of the usual transmission and control leads between a data modem and a data terminal are described, and examples are given of leased private-line and switched telecommunications network applications. A current look at the physical aspects of voice-band modems is given and future trends are considered.