Connecting intrinsically achiral catalytic centres to helical polymers provides a new class of asymmetric catalysts whose selectivity exclusively stems from the chiral environment provided by the helical polymer. Chirality amplification phenomena allow to control the handedness and the helical sense excess of these polymers which in turn dictate the stereochemical direction and the extent of enantioinduction, respectively, obtained in the course of the asymmetric reaction. This minireview is focused on such helical catalysts built either on a covalent or a non-covalent scaffold and for which the handedness is controlled by an asymmetric polymerization reaction, by enantiopure monomers or by chiral additives. The selectivity of catalysts based on a dynamic helical backbone can be controlled by changing the solvent or with additives. The fact that the enantiomeric state of such asymmetric catalysts can be switched in a predictable way is particularly emphasized.