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Atomic layer deposition (ALD), a chemical vapor deposition technique based on sequential self-terminating gas–solid reactions, has for about four decades been applied for manufacturing conformal inorganic material layers with thickness down to the nanometer range. Despite the numerous successful applications of material growth by ALD, many physicochemical processes that control ALD growth are not yet sufficiently understood. To increase understanding of ALD processes, overviews are needed not only of the existing ALD processes and their applications, but also of the knowledge of the surface chemistry of specific ALD processes. This work aims to start the overviews on specific ALD processes by reviewing the experimental information available on the surface chemistry of the trimethylaluminum/water process. This process is generally known as a rather ideal ALD process, and plenty of information is available on its surface chemistry. This in-depth summary of the surface chemistry of one representative ALD process aims also to provide a view on the current status of understanding the surface chemistry of ALD, in general. The review starts by describing the basic characteristics of ALD, discussing the history of ALD—including the question who made the first ALD experiments—and giving an overview of the two-reactant ALD processes investigated to date. Second, the basic concepts related to the surface chemistry of ALD are described from a generic viewpoint applicable to all ALD processes based on compound reactants. This description includes physicochemical requirements for self-terminating reactions, reaction kinetics, typical chemisorption mechanisms, factors causing saturation, reasons for growth of less than a monolayer per cycle, effect of the temperature and number of cycles on the growth per cycle (GPC), and the growth mode. A comparison is made of three models available for estimating the sterically allowed value of GPC in ALD. Third, the experimental information on the surface chemistry in the trimethylaluminum/water ALD process are reviewed using the concepts developed in the second part of this review. The results are reviewed critically, with an aim to combine the information obtained in different types of investigations, such as growth experiments on flat substrates and reaction chemistry investigation on high-surface-area materials. Although the surface chemistry of the trimethylaluminum/water ALD process is rather well understood, systematic investigations of the reaction kinetics and the growth mode on different substrates are still missing. The last part of the review is devoted to discussing issues which may hamper surface chemistry investigations of ALD, such as problematic historical assumptions, nonstandard terminology, and the effect of experimental conditions on the surface chemistry of ALD. I hope that this review can help the newcomer get acquainted with the exciting and challenging field of surface chemistry of ALD and can serve as a useful guide for the specialist towards the fifth decade of ALD research.