Atomic layer deposition (ALD) is gaining attention as a thin film deposition method, uniquely suitable for depositing uniform and conformal films on complex three-dimensional topographies. The deposition of a film of a given material by ALD relies on the successive, separated, and self-terminating gas-solid reactions of typically two gaseous reactants. Hundreds of ALD chemistries have been found for depositing a variety of materials during the past decades, mostly for inorganic materials but lately also for organic and inorganic-organic hybrid compounds. One factor that often dictates the properties of ALD films in actual applications is the crystallinity of the grown film: Is the material amorphous or, if it is crystalline, which phase(s) is (are) present. In this thematic review, we first describe the basics of ALD, summarize the two-reactant ALD processes to grow inorganic materials developed to-date, updating the information of an earlier review on ALD [R. L. Puurunen, J. Appl. Phys. 97, 121301 (2005)], and give an overview of the status of processing ternary compounds by ALD. We then proceed to analyze the published experimental data for information on the crystallinity and phase of inorganic materials deposited by ALD from different reactants at different temperatures. The data are collected for films in their as-deposited state and tabulated for easy reference. Case studies are presented to illustrate the effect of different process parameters on crystallinity for representative materials: aluminium oxide, zirconium oxide, zinc oxide, titanium nitride, zinc zulfide, and ruthenium. Finally, we discuss the general trends in the development of film crystallinity as function of ALD process parameters. The authors hope that this review will help newcomers to ALD to familiarize themselves with the complex world of crystalline ALD films and, at the same time, serve for the expert as a handbook-type reference source on ALD processes and film crystallinity.