A lubricant composition comprising: (i) a base oil; and (ii) an ethylene/a-olefin block interpolymer, wherein the ethylene/a-olefin block interpolymer comprises at least 80 mole.%, of the whole polymer, of ethylene; and has an Mw/Mn from 2.0 to 3.5, and (a) has 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) 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 ethylene/a-olefin block interpolymer, and has a density, d, in grams/cubic centimeter, wherein the numerical values of Re and d satisfy the following relationship when ethylene/a-olefin block interpolymer is substantially free of a cross-linked phase: Re > 1481 − 1629 d; or (d) has a comonomer content of the TREF fraction which elutes between 40°C and 130°C 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. (i) a base oil; and (ii) an ethylene/a-olefin block interpolymer, wherein the ethylene/a-olefin block interpolymer comprises at least 80 mole.%, of the whole polymer, of ethylene; and has an Mw/Mn from 2.0 to 3.5, and (a) has 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) 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 ethylene/a-olefin block interpolymer, and has a density, d, in grams/cubic centimeter, wherein the numerical values of Re and d satisfy the following relationship when ethylene/a-olefin block interpolymer is substantially free of a cross-linked phase: Re > 1481 − 1629 d; or (d) has a comonomer content of the TREF fraction which elutes between 40°C and 130°C 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. (a) has 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) 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 ethylene/a-olefin block interpolymer, and has a density, d, in grams/cubic centimeter, wherein the numerical values of Re and d satisfy the following relationship when ethylene/a-olefin block interpolymer is substantially free of a cross-linked phase: Re > 1481 − 1629 d; or (d) has a comonomer content of the TREF fraction which elutes between 40°C and 130°C 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.