The present invention provides solvent- and water-based primer compositions that include at least one carboxylated polyolefin that has been modified with one or more polyfunctional alcohols. The carboxylated polyolefins are obtained by the reaction of polyolefins with at least one of unsaturated carboxylic esters, unsaturated carboxylic acids, unsaturated carboxylic anhydrides, acrylic monomers, and mixtures thereof. The carboxylated polyolefins are then further modified by reaction with one or more polyfunctional alcohols. These polyfunctional alcohol-modified polyolefins may also contain pendant carboxyl groups, which have the propensity to form hydrophilic salts with amines or inorganic bases, thereby rendering the polyfunctional alcohol-modified polyolefins water-dispersible. These primer compositions are useful for significantly improving the adhesion of paints, adhesives, and inks to various plastic and metal substrates.