Embodiments of the invention provide a class of ethylene/.alpha.-olefin block interpolymers. The ethylene/.alpha.-olefin interpolymers are characterized by an average block index, ABI, which is greater than zero and up to about 1.0 and a molecular weight distribution, M.sub.w/M.sub.n, greater than about 1.3. Preferably, the block index is from about 0.2 to about 1. In addition or alternatively, the block ethylene/.alpha.-olefin interpolymer is characterized by having at least one fraction obtained by Temperature Rising Elution Fractionation ("TREF"), wherein the fraction has a block index greater than about 0.3 and up to about 1.0 and the ethylene/.alpha.-olefin interpolymer has a molecular weight distribution, M.sub.w/M.sub.n, greater than about 1.3.