The coating of complex three-dimensional structures with ultrathin metal films is of great interest for current technical applications, particularly in microelectronics, as well as for basic research on, for example, photonics or spintronics. While atomic layer deposition (ALD) has become a well-established fabrication method for thin oxide films on such geometries, attempts to develop ALD processes for elemental metal films have met with only mixed success. This can be understood by the lack of suitable precursors for many metals, the difficulty in reducing the metal cations to the metallic state, and the nature of metals as such, in particular their tendency to agglomerate to isolated islands. In this review, we will discuss these three challenges in detail for the example of Cu, for which ALD has been studied extensively due to its importance for microelectronic fabrication processes. Moreover, we give a comprehensive overview over metal ALD, ranging from a short summary of the early research on the ALD of the platinoid metals, which has meanwhile become an established technology, to very recent developments that target the ALD of electropositive metals. Finally, we discuss the most important applications of metal ALD.