Having replaced our disintegrating Brita pitcher a few years ago, I finally got around to opening a used filter to see what’s inside. Start by cutting off the flexible rim (intended as a seal against the pitcher) to reveal the joint, then pry the lid off:
Stand it upright before getting the lid off, because the filter contains a zillion charcoal granules and two zillion ion-exchange resin beads:
The inside of the lid has mesh screens to keep the innards in place while distributing the raw water:
Similarly, mesh on the bottom drains let the filtered water out:
No surprises, but now we all know what’s in there.
The Smell of Molten Projects in the Morning 
I have reverse osmosis filtration, and I recently opened an old membrane. It wasn’t very exciting.
I tried Walmart brand “For Brita” cartridges. Tiny bits of crap floated upward, out of the cartridge and into the unfiltered water area, but not in to the pitcher. Nevertheless this soured me on Brand X. I now use genuine Brita cartridges.
Even with the Official Cartridges, the first pitcher or two has a layer of carbon dust on the bottom, but I haven’t seen anything more than that. Bothers Mary more than me, so that’s when the pitcher gets a good washing; a little activated carbon filtering along my plumbing can’t possibly be a bad thing.