A polymer blend composition comprising: at least one ethylene/α-olefin interpolymer and at least one other polymer, wherein the ethylene/α-olefin interpolymer is a block interpolymer and (a) has a M w /M n from 1.7 to 3.5, at least one melting point, T m, in °C (degrees Celcius), and a density, d, in g/cm 3 (grams/cubic centimeter), wherein the numerical value of T m and d correspond to the relationship: T m > 2002.9 + 4538.5 d − 2422.2 d 2, or (b) has a M w /M n from 1.7 to 3.5, and is characterized by a heat of fusion, ΔH in J/g, and a delta quantity, ΔT, in °C (degrees Celsius), defined as the temperature difference between the tallest DSC peak and the tallest CRYSTAF peak, wherein the numerical values of ΔT and ΔH have the following relationships: Δ ⁢ T > 0.1299 ΔH + 62.81 for ΔH greater than zero and up to 130 J/g, Δ ⁢ T ≥ 48 ° C for ΔH greater than 130 J/g, wherein the CRYSTAF peak is determined using at least 5 percent of the cumulative polymer, and if less than 5 percent of the polymer has an identifiable CRYSTAF peak, then the CRYSTAF temperature is 30 °C; or (c) is characterized by an elastic recovery, Re, in percent at 300 percent strain and 1 cycle measured with a compression-molded film of the ethylene/α-olefin interpolymer, and has a density, d, in g/cm 3 (grams/cubic centimeter), wherein the numerical values of Re and d satisfy the following relationship when ethylene/α-olefin interpolymer is substantially free of a cross-linked phase: Re > 1481 − 1629 d; or (d) has a comonomer content of the TREF fraction greater than or equal to the quantity (- 0.2013) T + 21.07, where T is the numerical value of the peak elution temperature of the TREF fraction, measured in °C; or (e) has a storage modulus at 25 °C, G'(25 °C) and a storage modulus at 100 °C, G'(100 °C), wherein the ratio of G'(25 °C) to G'(100 °C) is in the range of 1:1 to 9:1; or (f) at least one molecular fraction which elutes between 40 °C and 130 °C when fractionated using TREF, characterized in that the fraction has a block index of at least 0.5 and up to 1 and a molecular weight distribution M w /M n, greater than 1.3. (a) has a M w /M n from 1.7 to 3.5, at least one melting point, T m, in °C (degrees Celcius), and a density, d, in g/cm 3 (grams/cubic centimeter), wherein the numerical value of T m and d correspond to the relationship: T m > 2002.9 + 4538.5 d − 2422.2 d 2, or (b) has a M w /M n from 1.7 to 3.5, and is characterized by a heat of fusion, ΔH in J/g, and a delta quantity, ΔT, in °C (degrees Celsius), defined as the temperature difference between the tallest DSC peak and the tallest CRYSTAF peak, wherein the numerical values of ΔT and ΔH have the following relationships: Δ ⁢ T > 0.1299 ΔH + 62.81 for ΔH greater than zero and up to 130 J/g, Δ ⁢ T ≥ 48 ° C for ΔH greater than 130 J/g, wherein the CRYSTAF peak is determined using at least 5 percent of the cumulative polymer, and if less than 5 percent of the polymer has an identifiable CRYSTAF peak, then the CRYSTAF temperature is 30 °C; or (c) is characterized by an elastic recovery, Re, in percent at 300 percent strain and 1 cycle measured with a compression-molded film of the ethylene/α-olefin interpolymer, and has a density, d, in g/cm 3 (grams/cubic centimeter), wherein the numerical values of Re and d satisfy the following relationship when ethylene/α-olefin interpolymer is substantially free of a cross-linked phase: Re > 1481 − 1629 d; or (d) has a comonomer content of the TREF fraction greater than or equal to the quantity (- 0.2013) T + 21.07, where T is the numerical value of the peak elution temperature of the TREF fraction, measured in °C; or (e) has a storage modulus at 25 °C, G'(25 °C) and a storage modulus at 100 °C, G'(100 °C), wherein the ratio of G'(25 °C) to G'(100 °C) is in the range of 1:1 to 9:1; or (f) at least one molecular fraction which elutes between 40 °C and 130 °C when fractionated using TREF, characterized in that the fraction has a block index of at least 0.5 and up to 1 and a molecular weight distribution M w /M n, greater than 1.3.