Hydrogen could play an important role as an energy vector in the coming decades in the framework of Sustainable Development. It is the universe's most abundant element and thus a never-ending source of energy. Hydrogen can be directly converted into electric energy by using fuel cells without producing toxic gases. It can also be produced by renewable sources such as biomass, solar and wind energies with no impact for the environment. However, although hydrogen represents a promising eco-friendly solution for energy transition, several issues related to its storage and delivery remain to be solved if it is to be widely used in both stationary and automotive applications. Hydrogen has the lowest volumetric energy density among the commonly used fuels, i.e., 0.01079 MJ/L at atmospheric pressure. Compression is the direct solution to overcome this obstacle. High pressure levels can give satisfying energy densities. The present review summarises the state of the art of the most classical hydrogen compression technologies. We shall present the technical and design features of mechanical compressors, i.e., reciprocating, diaphragm, linear and ionic liquid compressors, as well as of innovative non-mechanical technologies specifically conceived for hydrogen applications, such as cryogenic, metal hydride, electrochemical and adsorption compressors. The basic operating principles and the potential performance levels for each compression technology are analysed. Specifically, their current uses in hydrogen applications and their technological limits are described along with proposals of possible ways of improving their performance levels.