A foam comprising at least one ethylene/α-olefin block interpolymer, wherein the density of the foam is from greater than 150 to 500 kg/m 3 and wherein the ethylene/α-olefin block interpolymer: (a) has a M w /M n from 1.7 to 3.5, at least one melting point, T m, in °C (degrees Celsius), and a density, d, in g/cm 3 (grams/cubic centimeter), wherein the numerical values 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: 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 ethylene/a-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/a-olefin interpolymer is substantially free of a cross-linked phase: Re > 1481 − 1629 d; or (d) has a comonomer content of a TREF fraction which elutes between 40°C and 130°C greater than or equal to the quantity (-2013) T + 2107, 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. (a) has a M w /M n from 1.7 to 3.5, at least one melting point, T m, in °C (degrees Celsius), and a density, d, in g/cm 3 (grams/cubic centimeter), wherein the numerical values 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: 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 ethylene/a-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/a-olefin interpolymer is substantially free of a cross-linked phase: Re > 1481 − 1629 d; or (d) has a comonomer content of a TREF fraction which elutes between 40°C and 130°C greater than or equal to the quantity (-2013) T + 2107, 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.