Many useful organic reactions involve the formation of tetrahedral intermediates through nucleophilic attack of functional groups such as aldehydes, amides or imines. In these cases, catalysis with hydrogen-bond donors is an attractive strategy since the anionic tetrahedral intermediates are better hydrogen-bond acceptors than the starting compound. This means that relative to the initial catalyst-substrate complex, the transition state, bearing more negative charge, is stabilized.
For example, in a typical acyl substitution reaction, the starting carbonyl compound is coordinated to the catalyst through one, two or possibly more hydrogen bonds. During the attack of the nucleophile, negative charge builds on the oxygen until the tetrahedral intermediate is reached. Therefore, the formally negative oxygen engages in a much stronger hydrogen bond than the starting carbonyl oxygen because of its increased negative charge. Energetically, this has the effect of lowering the intermediate and the transition state, thus accelerating the reaction.
This mode of catalysis is found in the active sites of many enzymes, such as the serine proteases. In this example, the amide carbonyl is coordinated to two N–H donors. These sites of multiple coordination designed to promote carbonyl reactions in biology are termed "oxyanion holes". Delivery of serine nucleophile forms a tetrahedral intermediate, which is stabilized by the increase hydrogen bonding to the oxyanion hole. 
Many synthetic catalysts have been able to successfully employ this strategy to activate a variety of electrophiles. Using a chiral BINOL catalyst, for instance, the Morita-Baylis-Hillman reaction involving the addition of enones to aldehydes can be effected with high enantioselectivity. The nucleophile is an enolate-type species generated from the conjugate addition of PEt to the enone, and adds enantioselectively to the aldehyde coordinated to catalyst.
In addition to carbonyls, other electrophiles such as imines can be successfully used. For example, using a simple chiral thiourea catalyst, the asymmetric Mannich reaction of aromatic imines with silyl ketene acetals can be catalyzed with high ee in near quantitative conversion. The mechanism of this reaction is not fully resolved and the reaction is very substrate-specific, only effective on certain aromatic electrophiles. 
The scope of this mode of activation is immense, with constant new reports of different combinations of electrophiles, nucleophiles and catalyst structures. Furthermore, analogous reactions involving oxyanion intermediates such as enolate addition to nitroso compounds or opening of epoxides have also been successfully catalyzed with this strategy.
However, despite the number of different reactions known, general understanding of the mode of catalysis is limited, and almost all reactions discovered are extremely substrate specific.