I am Craft, and I am strong.

Just supposing we wanted to brew a really strong beer, how would we go about it?  Let's put aside the question of why we would want to do such a thing (I'll come back to that).

We could start with lots of malt.  Problem with that is, unless we're planning to leave a lot of extract on the grain, we'll just end up with a giant lot of regular strength wort.  Sure, we could boil it for hours and hours, but this is going to give us all sorts of unpleasant burnt notes in the beer (and, unless we're good at cleaning, in successive beers). We've all tasted that kind of thing.

We could use malt extract.  This is essentially wort made in a dedicated facility,  then concentrated, often under reduced pressure. We can buy it in big jugs (or in IBCs, if you want).  This is a pretty good way of going about it.  Obviously, you want to get most of your gravity from the contents of your mash tun, but in most strong beers, in my experience, we can go up to 20% malt extract without spoiling things.  Of course, 50kg of malt extract is hard to handle (it's terribly sticky and difficult to pour out for a start), but it can help make a reasonable amount of high-gravity wort without requiring more malt than would fit in the MT.

Malt extract has got a bit of a bad name among homebrewers.  The reasons are various, so I'll limit myself to pointing out that stuff that's been sitting in tin cans for months on warehouse shelves doesn't compare with the stuff that a commercial brewer will use.

We could add sugar.  This might be glucose, or even plain sucrose (which we can buy in big sacks from just down the road).  Of course, because these sugars are pretty much 100% fermentable, the resulting beer will be drier  (i.e. have less residual sweetness and a less heavy body) than an all-malt ,or malt extract, beer of the same alcoholic strength would be. Now sometimes, we'd want a beer to be lighter and drier - it goes to drinkability, which is why the the history of modern British brewing is, in a sense, a history of sugar.  Strong Belgian beers are marked by their use of sugars, it's that digestability thing, innit?

Again, homebrewers have reported all kinds of unpleasant effects which they put down to the use of sugar.  Of course, they've typically added a high proportion of sugar to a crappy malt-extract based kit (see above) and then bunged some crappy half-dead yeast into it, so I think we can safely discount most of that.

Because these tricks (adding sugars or malt extract) would enable us to get either stronger beer, or more beer, out of the same size kit, they're often called brewlength extenders.

We could, if we wanted to, add enzymes. Malt, of course, brings its own enzymes with it. (That's the point of malt).  But if we were using significant quantities of non-malt grain, we might choose to supplement with stuff from a bottle. Enzymes are often used in the MT to help get good conversion (starch into sugars) if we're brewing with a lot of, say, rice or maize. You generally find the enzymes called amylases used in this way. But these aren't the enzymes I'm interested in here.

When we boil our wort we effectively fix its sugar composition.  We destroy (or, technically, denature) the mash enzymes, so that the proportion of fermentable and non-fermentable components stays the same (until the yeast gets to work).  But we can, if we choose, add enzymes after the boil, in the fermenter or in a conditioning tank.  There are a few options open to the brewer who opts to follow this path, but the basic idea is that these enzymes break down the unfermentable "dextrins" and release fermentable sugars such as glucose. Upon which the yeast proceeds to chow down.  So it's the same basic idea as adding glucose.

There's a few gotchas associated with post-boil enzymes, following on from the fact that the sugar composition of our wort has been, now, unfixed:
Unless we pasteurise the beer these enzymes are going to carry on working until there are effectively no sweetening and body supporting dextrins left. None, nada, zilch, absolutely F.A. Hence, a fearsomely dry, thin, beer.
Also, in packaged products that contain live yeast, since fermentable sugars can continue being released by enzyme activity for quite some time (months?), there's a real danger of overconditioning. 

So, given that post-boil enzymes are difficult to control, somewhat risky, and can't produce better effects than adding, say, glucose, why would anyone use them?  In some cases, I suspect it's little more than marketing bullshit. We'd be able to say, "Look, here's a strong beer we made with only malt - no malt extract or sugar added!", conveniently neglecting to mention the Amyloglucosidase derived from a selected strain of Aspergillus.

But why set out to make a remarkably strong beer anyway?  I'm broadly in agreement with HardknottDave in his rhapsody on one of his own beers, strong beers do offer flavours that you just don't get in their smaller bretheren. We're not ashamed or afraid of alcohol, so don't see any need to make a beer weaker than it need be.  At the same time, I feel that we get into diminishing returns around 10% - and this is just a personal taste thing.  Over that level of alcohol, hot, even burny tones are difficult to avoid. Very strong beers are often too sweet, which I don't like, but that's probably better than them being burny with alcohol and too dry. I'm sure there are brewers who can pull it off, but I can't think of any off the top of my head. I'm sure extended (and I mean extended) aging will pull some of these beers together, but who's got time for that nowadays.  Again, it's often down to marketing bullshit.