I keep mine in the wrappers until the wrappers fall apart. After that, they’re out, but I keep the idea sheets over the blade side to help keep dust off them.
I have the 9” cube and it’s companion, but most of mine are individual dies that are stored in a couple of wire baskets that hang on my pegboard. The long 2.5” strip die is stored flat on the table behind my Sizzix Big Shot Pro.
I also have a number of paper and chipbaord cutting dies. To store those I repurposed a co uple of those plastic drawer units that used to hold VHS tapes.
Rob