Well I can talk to you about distortion in music mixing/engineering.
Distortion is the most useful tool of the mixing engineer, if you think about it you can only mix with distortion and EQ.
The first thing distortion does is coloring the sound and producing harmonics, The second thing is it compresses the sound in a more leveled fashion but judged by how much you distort the effect takes under consideration the actual dynamics, so, think about an envelope let's take a snare hit, the actual transient(or attack) gets really distorted and compressed, as the sound progresses and goes to sustain - decay the whole effect becomes more mellow.
Don't be afraid when distorting transients, there's no harm in it, the only thing you can trust in this is your ears.
Also distortion should be used everywhere, there's no bad distortion, even when you think a sound is trashed from it, try EQing to throw the junk/overtones away and mix it in parallel with the original signal to give that insane presence.
You have to keep in mind that any distortion effect is a non-linear effect!
Non linear in simple words mean that it can't be undone with the opposite, so for example if I take an EQ and boost 3K and right after use the same EQ but instead of boosting I use cut for the same exact amount, the sound remains unchanged right?
OK, now if you insert a non linear effect in the middle you never have the same sound again.
To explain myself, someone could say if I you use a compressor you'd also wouldn't have the same sound, well you would have the same sound but compressed, that said, distortion and non-linear effects change the core of the sound!
It's a very common practice (but not many people share it) to use EQ- non linear -EQ.
Let's use another example, let's say I really want to distort/alter a hihat, I go +30 db hi shelf -> distortion -> -30 db hi shelf (or according to taste). I managed to alter my sound in the frequency that I care about and then bring it back in a more normal (frequency-wise) state.
Distortion is super useful when mixing big bass! try this, distort your bass until you hear it going PRRRRRRRRRR, a point where you can actually hear the period of the singal, then just low pass it until you have the same effect but not the hi frequency trash. This creates a wide open and very well compressed bass.
Bass is the most sensitive area when distorting. It's the first thing that's gonna make you turn that knob back, sometimes it's your friend because if you have a nice balanced sound which just needs something extra, the bass is there to tell you when you've overdone it.
But, as we talked about pre-emphasis (or EQ - non linear - EQ) You can try pre emphasizing bass, which is actually what happens in the core of the audio transformer, try it on vocals, or on snare drums. I usually do it by really emphasizing close to 50 Hz and then taking it back.
In all of these FX chains the middle man is the non-linear friend, any type of distortion. Make your EQ and then just turn the knob to taste, it's the most intuitive knob in the studio!
Now, you might think I'm crazy, but these techniques are all over an analog studio, for example, dbx de-noiser is hi freq pre-emphasis -> compression -> Tape(non-linear) ->expansion -> hi freq de-emphasis. dbx has a lot of character, and I find it really cool! Also audio transformers core saturation is bass pre-emphasis - core saturation - de emphasis.and many many other examples.
Last super creative trick you can do, duplicate a track, distort the one, flip the phase to the other one and try to find the canceling spot with the fader (the place where you hear loss of sound and weird effects), playing a bit with this will drive you crazy when you think of the possibilities, this is called phase synthesis or at least I call it that way.
To sum everything up, distortion by itself is a self explanatory effect, when you put distortion in the middle of stuff it's the spice.
There are other very very interesting distortion effects such as crossover distortion or slew rate, but these are a bit deep for now!
The more of a friend you become with distortion the more it's going to sound better, there's that sweet spot, don't even think about it, start turning the knob, stop where you like, turn back if you think you over did it, and apply it to everything, if you have a clean mix, the distorted sound will be so full of frequencies it's just gonna jump out of the mix for fun.
Some last words. Distortion and general hi-end sound destruction is gonna make your sounds unbeatable by other stereos or cellphones or whatever, if you have a super clean sound, it's weak, a bad stereo will destroy it. If you have a hot signal (which doesn't mean the distortion is audible) it's like a signal on steroids, nothing can touch it, it fills the room, it's warm, it's punchy, it's everywhere!
Also ditch the bad distortions and super ditch the digital distortions (unless you want to go super creative), go to a studio with a good console one day, see what a neve does when you turn that line amp and start mixing.