Interesting that Kemper hasn’t been mentioned yet. They are a German company who make profiling amps, which basically consist of software able to profile an existing amplifier within ~2 minutes, and then perfectly replicating it. In an interview the inventor said that they have only on the order of 30 parameters which are configured during the profiling process, in which the device sends certain signals through the amplifier, and analyses the output. To make it stage-ready, it also has hundreds of effects and pedals (delay, wah, fuzz,...) on board.

Those Kemper profiling amps are widely used in the music industry, from hobbyists to absolute professionals. There are studios who profiled their 100s of custom amps with different mic pickup settings, and now only use the profiling amp instead. Paul Gilbert has one, and loves it, and he is reaaally picky about sound.

Apart from profiling your own amps, there is also a vast online library of profiles uploaded by community members. So if I want my amp to sound like Green Day, or just pick a certain amp like a Mark IV, I just search for that, load a matching profile into the profiling amp, and try it out. A plethora of parameters like gain can additionally be adjusted like on a normal amp - the profiling process somehow accounts for those parameters too.