Olefin polymer-based, durable, open-cell foam compositions, structures and articles derived from same; methods for preparation of such foams; and use of the dry durable foams in various applications are disclosed. Further described is use of the foams and structures and articles made of same in absorption, filtration, insulation, cushioning and backing applications, and in particular for odor removal, hygiene and medical applications due to, among other properties, good absorption capabilities, softness and/or flexibility of the foams and their recyclable nature.