###### Abstract  
Magnetic (Fe\({}_{3}\)O\({}_{4}\)) nanoparticles (NPs) are attractive nanomaterials in the field of material science, chemistry, and physics because of their valuable properties, such as soft ferromagnetism, half-metallicity, and biocompatibility. Various structures of Fe\({}_{3}\)O\({}_{4}\) NPs with different sizes, geometries, and nanoarchitectures have been synthesized, and the related properties have been studied with targets in multiple fields of applications, including biomedical devices, electronic devices, environmental solutions, and energy applications. Tailoring the sizes, geometries, magnetic properties, and functionalities is an important task that determines the performance of Fe\({}_{3}\)O\({}_{4}\) NPs in many applications. Therefore, this review focuses on the crucial aspects of Fe\({}_{3}\)O\({}_{4}\) NPs, including structures, synthesis, magnetic properties, and strategies for functionalization, which jointly determine the application performance of various Fe\({}_{3}\)O\({}_{4}\) NP-based systems. We first summarize the recent advances in the synthesis of magnetite NPs with different sizes, morphologies, and magnetic properties. We also highlight the importance of synthetic factors in controlling the structures and properties of NPs, such as the uniformity of sizes, morphology, surfaces, and magnetic properties. Moreover, emerging applications using Fe\({}_{3}\)O\({}_{4}\) NPs and their functionalized nanostructures are also highlighted with a focus on applications in biomedical technologies, biosensing, environmental remedies for water treatment, and energy storage and conversion devices. Fe\({}_{3}\)O\({}_{4}\) nanoparticles; magnetic properties; core-shell structures; nanocomposites; surface functionalization; biomedical applications; biosensing; environmental applications; energy storage 2021 2021 19 November 2021 29 November 202  
Web of Science, more than 41,000 research papers with the keyword \"Fe\({}_{3}\)O\({}_{4}\)\" have been published in the last 20 years, as shown in Figure 1. In the last 10 years, the number of these publications has increased drastically, with several hundred papers published per year. These numbers reflect the great attention given to Fe\({}_{3}\)O\({}_{4}\) nanomaterials by the research community in both fundamental studies and applied science. Fe\({}_{3}\)O\({}_{4}\) has attracted more attention than other iron oxides or ferrite spinel oxides (MFe\({}_{2}\)O\({}_{4}\) with M = Co, Ni, Mg, etc.) because of its superior magnetic properties, electronic conductivity, and biocompatibility. The magnetic properties of Fe\({}_{3}\)O\({}_{4}\) can be explained by its crystal structure. Magnetite has a cubic inverse spinel crystal structure consisting of Fe\({}^{2+}\) cations occupying 25% of the octahedral interstitial sites and Fe\({}^{3+}\) cations occupying 25% of the octahedral sites and 12.5% of the tetrahedral sites, and thirty-two O\({}^{2-}\) anions in its unit cell [20; 21]. The magnetic moments of Fe\({}^{3+}\) and Fe\({}^{2+}\) cations in octahedral holes are coupled ferromagnetically. However, the Fe\({}^{3+}\) ions in tetrahedral sites possess magnetic dipoles in the reverse direction of the Fe\({}^{3+}\) ions in the octahedral sites. Therefore, Fe\({}_{3}\)O\({}_{4}\) is a ferrimagnetic material with high saturation magnetization (M\({}_{S}\)) and low coercivity (H\({}_{C}\)) due to the antiferromagnetically coupled Fe\({}^{3+}\) cations in tetrahedral and octahedral sites of its crystal structure. Sometimes, the term ferromagnetic properties or ferromagnetism is also used for Fe\({}_{3}\)O\({}_{4}\), which indicates that it exhibits magnetic properties in the absence of a magnetic field. Regarding other iron oxide phases, maghemite is also a ferrimagnetic material, and hematite is considered a weak ferromagnetic material.