As methodology development matures it can be difficult to discern the most effective ways of performing certain transformations from the rest. This review summarizes the most important contributions leading to asymmetric hydrogenations of simple unsaturated-acid and ester substrates, with the objective of highlighting at least the best types of catalysts for each. Achievements in the area are described and these reveal situations where further efforts should be worthwhile, and ones where more research is only likely to give diminishing returns. In general, our conclusions are that the most useful types of catalysts for unsaturated-acids and -esters tend to be somewhat different, simple substrates have been studied extensively, and the field is poised to address more complex reactions. These could be ones involving alternative, particularly cyclic, structures, chemoselectivity issues, and more complex substrate stereochemistries.