This HOWTO currently only deals with the common type of modem used to connect PC's to ordinary analog telephone lines. There are various other types of modems, including devices called modems that are not really modems.
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 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 allowed on telephone circuits and this device is sometimes called a modem. This HOWTO doesn't cover such modems but some links to documents that do may be found at the start of this HOWTO. The next 3 sections: ISDN, DSL and 56k, concern digital-to-digital "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 section. Configuration might use "isdn-config" GUI. A Debian package "isdnutils" is available. There is a ISDN Howto in German with an English translation: http://sdb.suse.de/sdb/en/html/isdn.html. It's put out by the SuSE distribution of Linux and likely is about drivers available in that distribution. 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 (such as DejaNews) to find "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.
For any 56k modem to work as a 56k modem in your home or office, the other end must be connected directly to the digital system of the telephone company. Thus ISPs at the other end of the line must obtain special digital modems to provide customers with 56k service. There's more to it than this since banks of many modems are multiplexed onto a high capacity telephone cable that transports a large number of phone calls simultaneously (such as a T1, E1, ISDN PRI, or better line). This requires a concentrator or "remote access server". This has usually 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.
These are analog and not digital modems. These special modems are used on lines leased from the telephone company or sometimes on just a long direct wire hookup. Ordinary modems for a telephone line will not normally work on such a line. An ordinary telephone line has about 40-50 volts (known as the "battery) on it when not in use and the conventional modem uses this voltage for transmission. Furthermore, the telephone company has special signals indicating a ring, line busy, etc. Conventional modems expect and respond to these signals. Connecting two such modems by a long cable will not provide the telephone signals on the cable and thus the modems will not work.
A common type of leased line used two pairs of wires (one for each direction) using V.29 modulation at 9600 baud. Some brands of leased line modems are incompatible with other brands.