What MoS just said (Zip-Lock bags, sealed) is what we mostly do, but also what Aunty said (Airtight containers) with some things. We also have miller moths, and ants that invade from outdoors. They will exploit the tiniest crack or crevice.
Storage containers need to have a rubber seal around the lid or screw top.
Zip-lock bags need to be airtight as well, no pinholes or zippers that no longer seal.