The catalytic isomerization of propargylic alcohols promoted by transition-metals represents a straightforward and appealing route to synthetically useful alpha,beta-unsaturated carbonyl compounds. Three different reaction pathways are known for these atom-economical transformations: (i) the so-called Meyer-Schuster and Rupe rearrangements, in which a formal 1,3- or 1,2-shift of the hydroxyl group takes place, and (ii) the redox-type isomerization, which involves a simultaneous oxidation of the alcohol unit and reduction of the C[triple bond]C bond. In this Perspective article an overview of the different metal catalysts presently available to promote these isomerization reactions, their mechanisms of action as well as relevant synthetic applications, is provided.