Under one aspect, an elastically extensible cohesive article having first and second oppositely-facing major exterior surfaces includes a foam layer, and a cohesive composition coating at least a portion of each of the first and second major surfaces. The article may include a second layer, e.g., an elastic layer, an elastic fabric, a woven fabric, a knitted fabric, a non-woven fabric, or a second foam layer, juxtaposed with and secured to at least a portion of the foam layer. The foam layer may have a plurality of open cells that define at least a portion of one of the major exterior surfaces of the article, The open cells may act as "suction cups" that enhance the cohesive properties of the article, for example if the article is wrapped around a body part. The article may also include a pad that can be applied to a wound.