1962: Bell 103, 300 bit/s
AT&T's Bell 103 data set sent one bit per tone change: two frequencies for the calling end, two for the answering end. Some people learned to read it by ear, and it lasted decades in bulletin board systems and teletypes. Its ITU (then CCITT) cousin, V.21, uses the same idea on different frequencies and survives inside every modern handshake, carrying the V.8 menus.
1984–1988: V.22 and V.22 bis, 1200 and 2400 bit/s
Phase modulation arrived: instead of switching frequencies, the carrier's phase jumps between four (V.22) or sixteen (V.22 bis, with amplitude too) states, 600 times a second. The two directions still use separate bands, 1200 and 2400 Hz, so no echo canceller is needed.
1984 / 1991: V.32 and V.32 bis, 9600 and 14 400 bit/s
To go faster, both modems had to use the whole band at once, in both directions. That needs echo cancellation, which needs to know the line's round-trip delay, which is why V.32 starts with its ranging warble. V.32 bis added trellis coding and 14 400 bit/s.
1994: V.8 and V.34, 28 800 then 33 600 bit/s
V.34 measured the line before choosing how to use it: line probing with the 21-tone chord, a choice of six symbol rates and two carriers per direction, shell mapping and precoding. The handshake grew to several seconds. V.8 gave modems a common way to announce what they could do first, the CM/JM menus.
1998: V.90, 56 000 bit/s (downstream)
V.34 came close to what an analog line with G.711 quantization noise at both ends can carry (our summary; the limit is usually put at about 35 kbit/s). V.90's insight: if the server is on a digital line, there is only one conversion to analogue, at your end. The server sends exact codewords and your modem learns what each becomes, through the digital impairment learning bongs. The ITU's V.90 replaced two incompatible vendor schemes, x2 and K56flex.
2000: V.92, quick connect
V.92 let a modem remember the line from the last call and skip most of the handshake, plus modem-on-hold and faster upstream. The quick-connect handshake replaces the menus with a one-octet "we've met" signal and skips line probing.
After
ADSL used the same copper above the voice band, and the handshake noise disappeared from most homes within about a decade. The recommendations are still published by the ITU-T, free to read, which is what makes a site like this possible.