Methods are provided for refining natural oil feedstocks and producing isomerized esters and acids. The methods comprise providing a C4-C18 unsaturated fatty ester or acid, and isomerizing the fatty acid ester or acid in the presence of heat or an isomerization catalyst to form an isomerized fatty ester or acid. In some embodiments, the methods comprise forming a dibasic ester or dibasic acid prior to the isomerizing step. In certain embodiments, the methods further comprise hydrolyzing the dibasic ester to form a dibasic acid. In certain embodiments, the olefin is formed by reacting the feedstock in the presence of a metathesis catalyst under conditions sufficient to form a metathesized product comprising olefins and esters, separating the olefins from the esters in the metathesized product, and transesterifying the esters in the presence of an alcohol to form a transesterified product having unsaturated esters.