Like a couple of earlier posters said, I use adhesive magnetic strips inside a cupboard door in my craft room. Here's a photo of it:
Nestabilities storage by susanbri - Cards and Paper Crafts at Splitcoaststampers
This was taken a few years ago - I now have way more and the door is full and I've used the side wall of the cupboard as well!
For my smaller dies like a lot of the Memory Box ones, I use binders with the magnetic vent covers that earlier posters mentioned.