Westell Model 6100 AXXDSL DSL router. A digital subscriber line (DSL) modem is a device used to connect a computer or router to a telephone line which provides the digital subscriber line service for connectivity to the Internet, which is often called DSL broadband. DSL modems transfer data at a rate which is at least 10 to 20 times that of a voice-band modem. 2  DSL does not interfere with normal telephone calls on the telephone line, and does not require dialing a telephone number to initiate a connection, it is always on.