A modem (from modulate demodulate) is a device that modulates an analog carrier signal to encode digital information, and also demodulates such a carrier signal to decode the transmitted information. The goal is to produce a signal that can be transmitted easily and decoded to reproduce the original digital data. Modems can be used over any means of transmitting analog signals, from driven diodes to radio.

The most familiar example is a voiceband modem that converts the digital messages of a personal computer into sounds that can be transmitted over the telephone lines and once received, converts those sounds back into a digital format. Modems are generally classified by the amount of data they can send in a given time, normally measured in bits per second, or "bps". Faster modems are used by Internet users every day, notably cable modems and ADSL modems.

In telecommunications, "radio modems" transmit repeating frames of data at very high data rates over microwave radio links. Some microwave modems transmit more than a hundred million bits per second. Optical modems transmit data over optical fibers. Most intercontinental data links now use optical modems transmitting over undersea optical fibers. Optical modems routinely have data rates in excess of a billion (1x109) bits per second.

News wire services in the 1920s used multiplex equipment that met the definition, but the modem function was incidental to the multiplexing function, so they are not commonly included in the history of modems. George Stibitz connected a New Hampshire Teletype to a computer in New York City by phone lines in 1940, but the word "modem" had not yet been invented, so this too doesn't count.

Modems in the United States were first introduced as a part of the SAGE air-defense system in the 1950s, connecting terminals at various airbases, radar sites, and command-and-control centers to the SAGE director centers scattered around the U.S. and Canada. SAGE ran on dedicated communications lines, but the devices at each end were otherwise similar in concept to today's modems. IBM was the primary contractor for both the computers and the modems used in the SAGE system.

A few years later, a chance meeting between the CEO of American Airlines and a regional manager of IBM led to development of a "mini-SAGE" as an automated airline ticketing system. The terminals were at ticketing offices, tied to a central computer that managed availability and scheduling. The system, known as SABRE, is the ancestor of today's Sabre system.

For many years, AT&T maintained a monopoly in the United States on the use of its phone lines, allowing only AT&T-supplied devices to be attached to its network. For the growing group of computer users, AT&T introduced two digital sub-sets in 1958. One is the wideband device shown in the picture to the left. The other was a low-speed modem, which ran at 200 baud.

In the summer of 1960, the name Data-Phone was introduced to replace the earlier term digital subset. The 202 Data-Phone was a half-duplex asynchronous service that was marketed extensively in late 1960. In 1962, the 201A and 201B Data-Phones were introduced. They were synchronous modems using two-bit-per-baud phase-shift keying (PSK). The 201A operated half-duplex at 2000 bit/s over normal phone lines, while the 201B provided full duplex 2400 bit/s service on four-wire leased lines, the send and receive channels running on their own set of two wires each.

The famous 103A was also introduced in 1962. It provided full-duplex service at up to 300 baud over normal phone lines. Frequency-shift keying (FSK) was used with the call originator transmitting at 1070 or 1270 Hz and the answering modem transmitting at 2025 or 2225 Hz. The readily available 103A2 gave an important boost to the use of remote low-speed terminals such as the KSR33, the ASR33, and the IBM 2741. AT&T reduced modem costs by introducing the originate-only 113D and the answer-only 113B/C modems.