Amp modellers (and modelling amps, for that matter) have become hot guitar technology in recent years. Improvements in technology -- primarily, cheap, high-quality DACs -- have made amp modelers that sound good into the hands of both enthusiasts and professionals alike.
Consider: different styles of music usually require different guitar tones. You wouldn't put a high-gain rectifier on a blues record; nor would you, likely, put a warm, chunky, wall-of-sound Marshall stack on a metal album. Even within one genre, you might sometimes want to experiment with different tones -- that's what makes life interesting.
Before amp modellers, you'd have to be a millionaire with a room full of sweet-sounding vintage gear to have a variety of tones available to you. Not bloody likely.
Along comes Line 6. Well, not exclusively Line 6 (Hughes & Kettner, I am told, make some fine modelling amps), but they certainly helped make modelling amps cheap and popular. Their POD amp modeller is a desktop effect box capable of simulating (as of the 2.0 revision) 32 different amp classes, some vintage, some new hybrids. And it sounds sweet. Not perfect, of course -- nothing can really simulate a real tube amp -- but close enough.
Most amp modellers also include a speaker simulator. When recording an electric guitar, the last thing you want to do is go straight into the mixing board. You need to stick a mic in front of the speakers; a lot of the guitar's tone comes from the speakers. It's not always easy to get it right, though, and not always feasible. Have a home studio? Have neighbors? You get the idea. With a speaker simulator, you can run the guitar through the box right into the recording device -- what could be better?
But how does it work? Of course, Line 6 wouldn't give any details, their technology being a closely guarded trade secret. But, really, it's just EQ. Really, really good EQ, maybe a little multi-band compression, and probably some diodes to recreate overdrive and fuzz. I'd be willing to bet it's nothing more than that. But damn, it sounds good. And for the price -- the stand-alone POD retails around $300-350, while the combo amp models are about 2-3x that -- it can't be beat.
Of course, you just can't simulate all the nuances of tubes. There's a lot more entropy involved that creates interesting sounds and dynamic compression effects. But you can get pretty close with an amp modeller, and it won't break the bank. Bands are starting to use them on the road -- Weezer, for one, on their latest tour, to save space and money on additional trucks -- and even in the studio (XTC, for example).
Purists may hail the wonders of tubes, but I'd rather save the cash and buy a better axe or two, instead of a space-hogging amp.