Chiral bifunctional dual H-bond donor catalysts have become one of the pillars of organocatalysis. They include squaramide, thiosquaramide, thiourea, urea, and even selenourea-based catalysts combined with chiral amines, cinchona alkaloids, sulfides, phosphines and more. They can promote several types of reactions affording products in very high yields and excellent stereoselectivities in many cases: conjugate additions, cycloadditions, the aldol and Henry reactions, the Morita-Baylis-Hilman reaction, even cascade reactions, among others. The desire to understand mechanisms and the quest for the origins of stereoselectivity, in attempts to find guidelines for developing more efficient catalysts for new transformations, has promoted many mechanistic and theoretical studies. In this review, we survey the literature published in this area since 2015.