The research on complex hydrides for hydrogen storage was initiated by the discovery of Ti as a hydrogen sorption catalyst in NaAlH₄ by Boris Bogdanovic in 1996. A large number of new complex hydride materials in various forms and combinations have been synthesized and characterized, and the knowledge regarding the properties of complex hydrides and the synthesis methods has grown enormously since then. A significant portion of the research groups active in the field of complex hydrides is collaborators in the International Energy Agreement Task 32. This paper reports about the important issues in the field of complex hydride research, i.e. the synthesis of borohydrides, the thermodynamics of complex hydrides, the effects of size and confinement, the hydrogen sorption mechanism and the complex hydride composites as well as the properties of liquid complex hydrides. This paper is the result of the collaboration of several groups and is an excellent summary of the recent achievements.