The old tub was surrounded by tile. The way you're supposed to install this is to put some sort of vapor barrier (plastic sheeting) on the studs, put up some sort of cement backerboard over that, and then set the tile on the backerboard. All nice and moisture proof for the wet area.
This is not the way this was done. Instead, the walls around the tub were made of something called "greenboard", and there was no vapor barrier. Greenboard is a water-resistant form of drywall. It won't be damaged by water (much), but it's POROUS. Tile grout is also not waterproof. So over the years, humidity slowly seeped through the tile and greenboard. The result? Well, see for yourself.

Nasty mildew in the insulation. All that insulation had to come out.

These strips of
plastic in the corner are the only thing resembling a vapor barrier that was installed.