I love cyanoacrylate adhesives. With paper/cardboard you get a composite that's almost fiberglass. With nylon (anything from stockings to ripstop) you get even closer. Or silk or kevlar. All of them react exothermically with cyanoacrylate, so they cure very quickly.
Also, bizarrely enough, fine brass wool. I used that to fill a large gap in the rim of a pottery coffee mug. That repair has lasted over five years. Including microwaving multiple times daily to warm coffee.
I use it mainly for plastics, where it works very well (I managed to break the plastic before the CA bond). However, yesterday I had one fail when I used it in the sink (and thus was wet a lot). I have no idea why water ruined the bond, but I used an epoxy for it and hope it will be okay now.
Cyanoacrylate works well with plastics that it dissolves. So it's like solvent weld plus glue. Polystyrene, polycarbonate and PVC, for example. Or materials with hydroxyl groups, with which it reacts. Such as paper, wood, silk, rayon, nylon and kevlar. But not polyethylene.
And not polystyrene foam, because it melts it. My favorite for that is Gorilla Glue. I don't know what's in it. But it has something that reacts with water (which is the catalyst) and also the same materials that cyanoacrylate works well with. But it doesn't melt the foam, just melds with it.
For polystyrene foam, I use UHU Por (not sure what the chemical is), it makes it brand new. I have an EPP wing that I crashed three times and broke into pieces, and Por makes it brand new again.
The bond that failed was PLA to PLA (I 3D-printed a soap holder, so the surface wasn't very smooth either). I don't know if it was the water or if I didn't apply enough glue or what.
Water is also a catalyst to cyanoacrylate. The trouble is cyanoacrylate cures instantly, so if the surface is at all wet the glue doesn't get a chance adhere to the surface - it solidifies instantly on contact with the water.
When I'm in a hurry, I touch edges of a joint with a slightly damp piece of cotton. A polymerization wave then sweeps through the joint. As I vaguely recall, that's how we used to set polyamide resin for boat repairs.
