A polymer composition comprises at least an ethylene/.alpha.-olefin interpolymer and at least one other polymer. The other polymer can be selected from a second ethylene/.alpha.-olefin interpolymer, an elastomer, a polyolefin, a polar polymer, and an ethylene/carboxylic acid interpolymer or ionomer thereof. The ethylene/.alpha.-olefin interpolymer is a block copolymer having at least a hard block and at least a soft block. The soft block comprises a higher amount of comonomers than the hard block. The block interpolymer has a number of unique characteristics disclosed here. Also provided are gaskets, bottle cap liners, and closures that comprise or obtained from a compositon comprising at least one ethylene/.alpha.-olefin interpolymer and at least one polyolefin. The gaskets are capable of compression sealing various containers, without contaminating the contents. Liquid containers particularly benefit from the use of the novel gasket materials disclosed herein.