The rational design of small but highly functional artificial catalysts is very important for practical organic synthesis. Asymmetric Lewis acid catalyses with non-covalent secondary interactions have been developed for enantioselective reactions. This tutorial review describes the concept, design and examples of asymmetric Cu(ii) catalyses for cycloaddition reactions based on intramolecular π-cation or n-cation interactions between the copper(ii) cation and auxiliary Lewis basic sites of the chiral ligands.