This invention relates to a composition comprising a functionalized C3 to C40 olefin polymer comprising at least 50 mol % of one or more C3 to C40 olefins, and where the olefin polymer, prior to functionalization, has: a Dot T-Peel of 1 Newton or more on Kraft paper; an Mw of 10,000 to 100,000; and a branching index (g′) of 0.98 or less measured at the Mz of the polymer when the polymer has an Mw of 10,000 to 60,000, or a branching index of 0.95 or less measured at the Mz of the polymer when the polymer has an Mw of 10,000 to 100,000; and where the C3 to C40 olefin polymer comprises at least 0.001 wt % of a functional group. This invention further relates to blends of such functionalized polymers with other polymers including non-functionalized C3 to C40 olefin polymers as described above.