Hello!

I found one of the bobbleheads but it's been stuck in my inventory every since. Whenever I try and place it or remove it from my inventory it tells me it cannot be done because it's a quest item. Have I missed something with it? Am I meant to hand it in or use it in some way?

On a side question, what do they actually do?

Thanks

You can build a Bobblehead stand at a settlement, I believe that's the only way to display them and get them out of your inventory.

Each one (I think there are 20 in total) gives you a perk of some description, but like with magazines you don't need to keep them in your inventory once you've picked them up.