Recent progress on our Brønsted acid/Lewis base hybrid complexes in some asymmetric catalyses is reviewed. Based on the rational design of conjugated acid–base catalysts, tailor-made supramolecular catalysts can show remarkable catalytic activity and higher-ordered selectivities that cannot be realized by ready-made single-molecule catalysts. The chiral supramolecular magnesium(II) binaphtholate complexes trigger the highly enantioselective 1,4-hydrophosphinylation and 1,2-hydrophosphonylation of α,β-unsaturated carbonyl compounds, direct Mannich-type reaction, and hetero-Diels–Alder reaction. Moreover, the advanced supramolecular catalysts are prepared in situ from chiral 3,3′-disubstituted binaphthols and biphenols, arylboronic acid, and B(C6F5)3, for promoting the anomalous endo-/exo-selective Diels–Alder reaction. The specific mechanism and deep insights into the possible key intermediates are discussed on the basis of rational design of chiral supramolecular Brønsted acid/Lewis base hybrid catalysts as artificial enzymes.