Abstract Rare earth metal oxide nanomaterials have drawn much attention in recent decades due to their unique properties and promising applications in catalysis, chemical and biological sensing, separation, and optical devices. Because of the strong structure–property correlation, controllable synthesis of nanomaterials with desired properties has long been the most important topic in nanoscience and nanotechnology and still maintains a grand challenge. A variety of methods, involving chemical, physical, and hybrid method, have been developed to precisely control nanomaterials, including size, shape, dimensionality, crystal structure, composition, and homogeneity. These nanostructural parameters play essential roles in determining the final properties of functional nanomaterials. Full understanding of nanomaterial properties through characterization is vital in elucidating the fundamental principles in synthesis and applications. It allows researchers to discover the correlations between the reaction parameters and nanomaterial properties, offers valuable insights in improving synthetic routes, and provokes new design strategies for nanostructures. In application systems, it extrapolates the structure–activity relationship and reaction mechanism and helps to establish quality model for similar reaction processes. The purpose of this chapter is to provide a comprehensive overview and a practical guide of rare earth oxide nanomaterial design and characterization, with special focus on the well-established synthetic methods and the conventional and advanced analytical techniques. This chapter addresses each synthetic method with its advantages and certain disadvantages, and specifically provides synthetic strategies, typical procedures and features of resulting nanomaterials for the widely-used chemical methods, such as hydrothermal, solvothermal, sol–gel, co-precipitation, thermal decomposition, etc. For the nanomaterial characterization, a practical guide for each technique is addressed, including working principle, applications, materials requirements, experimental design and data analysis. In particular, electron and force microscopy are illuminated for their powerful functions in determining size, shape, and crystal structure, while X-ray based techniques are discussed for crystalline, electronic, and atomic structural determination for oxide nanomaterials. Additionally, the advanced characterization methodologies of synchrotron-based techniques and in situ methods are included. These non-traditional methods become more and more popular because of their capabilities of offering unusual nanostructural information, short experiment time, and in-depth problem solution. Graphical Abstract:
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