The reductive amination, the reaction of an aldehyde or a ketone with ammonia or an amine in the presence of a reducing agent and often a catalyst, is an important amine synthesis and has been intensively investigated in academia and industry for a century. Besides aldehydes, ketones, or amines, starting materials have been used that can be converted into an aldehyde or ketone (for instance, carboxylic acids or organic carbonate or nitriles) or into an amine (for instance, a nitro compound) in the presence of the same reducing agent and catalyst. Mechanistically, the reaction starts with a condensation step during which the carbonyl compound reacts with ammonia or an amine, forming the corresponding imine followed by the reduction of the imine to the alkyl amine product. Many of these reduction steps require the presence of a catalyst to activate the reducing agent. The reductive amination is impressive with regard to the product scope since primary, secondary, and tertiary alkyl amines are accessible and hydrogen is the most attractive reducing agent, especially if large-scale product formation is an issue, since hydrogen is inexpensive and abundantly available. Alkyl amines are intensively produced and use fine and bulk chemicals. They are key functional groups in many pharmaceuticals, agro chemicals, or materials. In this review, we summarize the work published on reductive amination employing hydrogen as the reducing agent. No comprehensive review focusing on this subject has been published since 1948, albeit many interesting summaries dealing with one or the other aspect of reductive amination have appeared. Impressive progress in using catalysts based on earth-abundant metals, especially nanostructured heterogeneous catalysts, has been made during the early development of the field and in recent years.