Being both an insane Subaru guy as well as a diesel Powerstroke guy, I'm willing to pollute your mind.
Basically, both water and methanol (but especially methanol) injection provides cylinder charge cooling on turbosupercharged vehicles, due to the adiabatic expansion cooling and heat absorption that occurs with the injection.
My fanboy love of turbosupercharging (I say this because i was once a professor of such things... it's ALL supercharging, [added air] but when the exhaust drives it (opposed to a mechanical belt or gear drive [Mad Max] it's TURBOsupercharging... Gosh I rant, sorry).
The deal is that when you compress things they get hot. Hot bad. Hulk smash, or at least melt pistons. Intercool to the most you can possibly do, but the bottom line is that at high CFM consumption you may not get the cooling you need for the "dyno bragging rights" you may (or may not) have moist dreams about.
Enter various sprays of stuff, hydrocarbons, water, especially alcohols. Alcohols (ETOH [my favorite] and methanol [second favorite, but blindness and insanity (plus death) really sucks]) have amazing cooling effects when sprayed at the right amount and pressure to create the right droplet size.
Us Scoobydoo geeks sometimes consider running E85, which is probably only 80% corn liquor (aka ETOH, vodka, moonshine, corn-shot, etc.. the rest is petrol), or meth injection (super poisonous, and quite expensive) but an interesting note is that both alcohols have a much lower BTU content than gasoline. However, the cooling effect allows wicked fun compression levels. That fun comes at a cost of reduced availability and expensive juice. Top fuel dragsters use the methanol variety of alcohol, which is wicked fast (due to the cooling) but also has a limited BTU content. And there's simply not enough orange juice, ever. Don't drink it.
[Sorry, my laptop battery died and I didn't finish. And I have so much more to say [cough] ...]
The POINT is, that compression creates heat. It doesn't matter whether that comes from a roots supercharger, a centrifugal supercharger, or any one of dozens of turbosuperchargers that compress the intake oxygen. And then...
THEN, those silly pistons compress even more. Maybe only 8:1 on a turbo car (because of the heat, not the stress). Again, compress a gas and you get heat. Geeks may want to reference Boyle's Ideal Gas Law. (This in the 1600's, before anybody knew anything about anything. Yet this bloke knew way much. An understanding of his basic premise 400+ years ago is a really nice tool in your box.)
Okay, so what? Everything is fine as long as the ignition event occurs when it's designed to (diesel or petrol, alcohol spray or pure). When you compress and heat too much before the scheduled ignition event, you might ping. Knock,ping, predetonation; the devil has many names. You don't want your fuel charge igniting too much before TDC on compression (A little, that's okay as advance) such that the piston wants to spin the engine backwards.
First of all, you get no power. Second of all, you start putting stresses on the reciprocating system like no other. You can ruin an engine quickly in this mode, from the heat and the bassackwards BMEP.
So, keep it squeezed, but keep it cool so there is no pre-detonation. That's where a really good "tune" comes in.
If you can't intercool the intake charge enough for your desired power levels and prevent "knock" (pre-detonation), you need to spray water, or ethanol or methanol, or use mostly ethanol or methanol in the first place.
If your budget or circumstances don't allow E85 fuel tank fills or methanol poison sprays, you probably need to reduce "boost" to a point that precludes knock, or be prepared to rebuild every 5-10k.
Whatever you do, you need a "tune" that can instantly recognize cattywompus AFR and exhaust gas temperatures, and back out of the mix before catastrophic engine failure. You might only have a few dozen revolutions for your computer to do this.
(3a) Whatever you do, you need the flexibility to switch to RON 95 petrol in the middle of Des Moines at 2am when nothing else is available.
On the emissions side of things, even high non-destructive heat creates oxides of Nitrogen, which a basic three-way catalytic converter may have trouble dealing with. While a "proper" stochiometric burn around 14:1 AFR might prevent engine damage, that also doesn't provide as much power. Hotter is better, as long as you can get rid of the heat before you damage things. this is where Gasoline Direct Injection (GDI) has come into play (Skyactive, Blue, Powerboost, whatever) has really made some serious IC advances. With the inherent cost of a separate catalyst to deal with NOx, and urea "DEF" injection for diesels. NOx is basically "smog". Lean burn means more power, but we are expected to deal with our "emissions" in a proper way.
Diesels follow some of the same logic, but are different in that they inherently use BMEP to create the combustion event... although it's direct injection technology that also has a huge effect on timing.
In the case of diesel, I'm a big fan of liquid propane as the right stuff. Not only does this have that adiabatic cooling effect, it also has BTU content. Water does not. Propane is the Nitrous Oxide for diesels. And Nitrous Oxide injection also has that cooling effect. (Not to be confused with "Nitric Oxide", which is the subject of Viagra and similar and has to do with performance of other equipment... )