Embodiments of the invention provide a class of butene/α-olefin block interpolymers. The butene/α-olefin inter-polymers are characterized by an average block index, ABI, which is greater than zero and up to about 1.0 and a molecular weight distribution, Mw/Mn, greater than about 1.3. Preferably, the block index is from about 0.2 to about 1. In addition or alternatively, the block butene/α-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 butene/α-olefin interpolymer has a molecular weight distribution, Mw/Mn, greater than about 1.4.