Covered, but not airtight or waterproof.
My current rotation is:
Tabac in a ceramic bowl with the red lid... the lid has "dimples" that hold the lid off of the bowl
MWF in it's ceramic bowl/lid. Lid has no dimples, but it's certainly not "anything proof"
Mama Bear's in her wooden bowl. This one stays on the bottom of the stack because the lid warps if I don't keep weight on it.
I just got some Ogallala bay rum soap and an aluminum tin for storing it. It has a screw-cap with a gasket, but I'll likely leave the lid loose.
I try to order my soaps, whenever possible, with a container with a lid as it's just more convenient for stacking and storing that way. If I don't have a container with a lid, though, I leave them in the open. I currently have a mug with HBS Sandalwood and a ramekin with an Arko stick out in the open.
Hoping to tone down the scent on the Arko a bit.
I cover the ones with lids. The mugs and bowls that do not have lids, I turn them upside down when sitting on the shelf. My house is really dusty from blow fill insulation in the attic. I really need to get that changed over.