I'm very low-tech. Most of my necklaces are in individual tiny zip-top bags, tossed in a pouch and stored in a safe. Keeping a small bit of the chain outside the sealed bag seems to help prevent the rest from knotting itself up.
Necklaces are in my current rotation, I hang on this Command Hook jewelry rack and it's kept every one within reach and no tangles to deal with!
I have a Gerstner industrial chest, affectionately renamed the treasure chest. I bought felt covered ring and earring holders that fit perfectly in the drawers. Necklaces and bracelets lay flat. The top holds watches and projects.
The 2007 is a portable, felt-lined wood tool chest, inspired by the popular Style 41 & modernized for today's craftsman & collector. Expert-made in the USA.