The paper is a review of techniques for the transmission of medium-speed data over ionospheric channels. Typical applications are digital voice and high integrity data transmission using normal voice bandwidth circuits. The characteristics of the fading multipath propagation channel are described, as well as the relevant radio equipment limitations. An historical overview of modem designs is included from the early multitone designs to the present day. The two basic design approaches of multiple low-speed channels and a single high symbol rate channel with adaptive processing are described. The impact of new digital signal processing technology on modem implementation is noted. The performance of the different designs is compared, both on theoretical grounds and from the results of practical measurements. It is concluded that the single tone approach generally offers superior performance in terms of lower bit error rates, but the choice is highly dependent on the application.