Early modems used frequency shift keying. Later modems used first phase shift keying and then quadrature amplitude modulation to give progressively higher performance.
Modern audio modems (V.90 and V.92 standards) closely approach the [Shannon capacity]? of the PSTN telephone channel.
ADSL modems are also a kind of modem, the main difference being that they are not limited to audio frequencies over the telephone line. Recent ADSL modems use coded orthogonal frequency division modulation.
See modulation for a fuller list of modulation techniques.