I have a Mighty Wallet, which is basically a Folded tyvek sheet.
Because it's tyvek it's light and stupid durable. Their marketing material had them suspending their body weight from them and other feats
Because it's origami it automagically expands and contracts to suit how much I put in it so it always stays low profile. Again, their marketing material had them taking an empty wallet, which is pretty much flat. Stuffing it full of douzens of business cards, ballooning the wallet to accommodate the volume. Then when they removed the stuff the wallet went back to being flat.
They also did custom designs, what I had printed makes my wallet look like it's made of paper. It's also very thin material, everyone thinks they can tear it... no one has.
Cons: It was pricey for a folded plastic sheet, they offered the net for free so you could make your own. No coin pouch. I have had things fall out/swap pocket when I opened the wallet. It has been through the washing machine more than any other wallet I've owned because I miss it.