This HOWTO only deals with the common type of analog modem used to connect PC's to ordinary analog telephone lines. The standard definition of a modem is sometimes broadened to include digital "modems". Today direct digital service is now being provided to many homes and offices so that a computer there sends out digital signals directly (well almost) into the telephone lines. But a device is still needed to convert the computer digital signal into the type of digital signal used telephone circuits. This device is sometimes called a modem. While this HOWTO doesn't cover such modems, some links to documents that do may be found at the start of this HOWTO. The next 3 sub-sections: ISDN, DSL and 56k, briefly mention such "modems".
Such a "modem" is really a Terminal Adapter (TA). Support for some of them can be built into the kernel 2.4 or added as a module. The kernel documentation has an isdn subdirectory. Configuration might use "isdn-config" GUI. A Debian package "isdnutils" is available. There is SuSE ISDN Howto (not a LDP Howto) which is translated from German http://sol.parkland.cc.il.us/sdb/en/html/isdn.html There is an isdn4linux package and a newsgroup: de.alt.comm.isdn4linux. Many of the postings are in German. You might try using a search engine to look for "isdn4linux".
DSL uses the existing twisted pair line from your home (etc.) to the local telephone office. This can be used if your telephone line can accept significantly higher speeds than an ordinary modem would use. It replaces the analog-to-digital converter at the local telephone office with a converter which can accept a much faster flow of data (in a different format of course). The device which converts the digital signals from your computer to the signal used to represent digital data on the local telephone line is also called a modem.
These are not the 56k modems that people use in their PCs. They are the "modems" at an ISP that these 56k modems connect to. The ISP must be connected directly to the digital system of the telephone company, otherwise the customers modem can't be used as a 56k modem. The ISP likely has banks of many modems multiplexed onto a high capacity telephone cable that transports a large number of phone calls simultaneously (such as a T1, E1, ISDN PRI, etc.). This requires a concentrator or "remote access server" (RAS). This has previously been done by stand-alone units (like PC's but they cost much more and have proprietary OSs). Now there are some cards one may insert into a PC's PCI bus to do this. See Digital Modems)