An impact modified composition comprising: A) a thermoplastic polymer composition; and B) an impact-modifying amount of a multi-block ethylene/a-olefin interpolymer comprising hard segments and soft segments, wherein the amount of the hard segments is from 35 weight percent to 50 weight percent, based on the total weight of the multi-block ethylene/a-olefin interpolymer, and wherein the multi-block ethylene/a-olefin interpolymer: (a) has a Mw/Mn from 1.7 to 3.5, at least one melting point, Tm, in degrees Celsius, and a density, d, in grams/cubic centimeter, wherein the numerical values of Tm and d correspond to the relationship: T m > − 2002.9 + 4538.5 d − 2422.2 d 2; or (b) has a Mw/Mn from 1.7 to 3.5, and is characterized by a heat of fusion, ΔH in J/g, and a delta quantity, ΔT, in 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: ΔT > -0.1299(ΔH) + 62.81 for ΔH greater than zero and up to 130 J/g, ΔT ≥ 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 multi-block ethylene/a-olefin interpolymer, and has a density, d, in 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 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; or (e) has an average block index greater than zero and up to 1.0 and a molecular weight distribution, Mw/Mn, greater than 1.3; or (f) 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. A) a thermoplastic polymer composition; and B) an impact-modifying amount of a multi-block ethylene/a-olefin interpolymer comprising hard segments and soft segments, (a) has a Mw/Mn from 1.7 to 3.5, at least one melting point, Tm, in degrees Celsius, and a density, d, in grams/cubic centimeter, wherein the numerical values of Tm and d correspond to the relationship: T m > − 2002.9 + 4538.5 d − 2422.2 d 2; or (b) has a Mw/Mn from 1.7 to 3.5, and is characterized by a heat of fusion, ΔH in J/g, and a delta quantity, ΔT, in 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: ΔT > -0.1299(ΔH) + 62.81 for ΔH greater than zero and up to 130 J/g, ΔT ≥ 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 ΔT > -0.1299(ΔH) + 62.81 for ΔH greater than zero and up to 130 J/g, ΔT ≥ 48°C for ΔH greater than 130 J/g, (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 multi-block ethylene/a-olefin interpolymer, and has a density, d, in 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 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; or (e) has an average block index greater than zero and up to 1.0 and a molecular weight distribution, Mw/Mn, greater than 1.3; or (f) 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.