A overglorified SoundCard masquerading as a MoDem. The hardware consists of little else than a DAC/ADC, whereas the actual signal processing logic is performed by the host computer's CPU. The software masquerades as a "driver", which is generally available from vendors only for MicrosoftWindows.
Fortunately there are increasingly more WinModem drivers available for Linux. Supported MoDems get affectionately called 
LinModems. Beware though, there are only few of these among the WinModems.
Intel now has a supported WinModem chipset (DSE sells MoDems based on these) and because they have both MicrosoftWindows and Linux drivers Intel calls them HaM, "Host-accelerated Modem". How a 56K WinModem is "accelerated" in comparison to a 56k hardware modem isn't entirely clear; this appears to be MarkeTroid speak.
The MWave WinModem in IBM ThinkPads is also supported. IBM released the driver under GPL, so it has made its way into the official Kernel source tree.
By far the most common WinModems (at least in NewZealand) are ones based on Conexant chipsets. For a long time there was no way at all to get any of these to work in Linux, but at some point they released Linux drivers.
If you want to get a new MoDem for a Linux and would like to avoid the cost of a hardware MoDem, 
DanielLawson recommends a Lucent or Agere compatible chipset based WinModem, after good experience with a Lectron I56LVP/F4 ($32 as of May 2004) that runs fine with the ltmodem drivers. If the binary Package doesn't work for you, get the source package and follow the instructions, there's a couple of scripts you can run which basically automate the whole installation.
Some modern distros include drivers for the more common WinModems.
4 pages link to WinModem:
