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Colloidal nanoparticles are being intensely pursued in current nanoscience research. Nanochemists are often frustrated by the well-known fact that no two nanoparticles are the same, which precludes the deep understanding of many fundamental properties of colloidal nanoparticles in which the total structures (core plus surface) must be known. Therefore, controlling nanoparticles with atomic precision and solving their total structures have long been major dreams for nanochemists. Recently, these goals are partially fulfilled in the case of gold nanoparticles, at least in the ultrasmall size regime (1-3 nm in diameter, often called nanoclusters). This review summarizes the major progress in the field, including the principles that permit atomically precise synthesis, new types of atomic structures, and unique physical and chemical properties of atomically precise nanoparticles, as well as exciting opportunities for nanochemists to understand very fundamental science of colloidal nanoparticles (such as the stability, metal-ligand interfacial bonding, ligand assembly on particle surfaces, aesthetic structural patterns, periodicities, and emergence of the metallic state) and to develop a range of potential applications such as in catalysis, biomedicine, sensing, imaging, optics, and energy conversion. Although most of the research activity currently focuses on thiolate-protected gold nanoclusters, important progress has also been achieved in other ligand-protected gold, silver, and bimetal (or alloy) nanoclusters. All of these types of unique nanoparticles will bring unprecedented opportunities, not only in understanding the fundamental questions of nanoparticles but also in opening up new horizons for scientific studies of nanoparticles.