Software defined radio is a method of radio which attempts to do as much as possible in the digital realm, and the least amount in hardware. Ultimately they will digitize the spectrum the way a soundcard does, and use software to filter and demodulate the signals.
There's a decent
intro to software defined radio and
a dozen or so online quadrature sampling sdrs that you can click to listen to.
The filtering is very slick. I saw a demo of an AM filter that completely removes interference from off-frequency stations. Imagine listening to an AM broadcast buried between two stations playing music, clicking on the filter, and the interference goes away...