Some of the synthesis methods and physical properties of iron oxide-based magnetic nanoparticles such as Fe3-xO4 and CoxFe3-xO4 are reviewed because of their interest in health, environmental applications, and ultra-high density magnetic recording. Unlike high crystalline quality nanoparticles larger than a few nanometers that show bulk-like magnetic and electronic properties, nanostructures with increasing structural defects yield a progressive worsening of their general performance due to frozen magnetic disorder and local breaking of their crystalline symmetry. Thus, it is shown that single-crystal, monophasic nanoparticles do not exhibit significant surface or finite-size effects, such as spin canting, reduced saturation magnetization, high closure magnetic fields, hysteresis-loop shift or dead magnetic layer, features which are mostly associated with crystallographic-defective systems. Besides, the key role of the nanoparticle coating, surface anisotropy, and inter-particle interactions are discussed. Finally, the results of some single particle techniques -magnetic force microscopy, Xray photoemission electron microscopy, and electron magnetic chiral dichroism-that allow studying individual nanoparticles down to sub-nanometer resolution with element, valence and magnetic selectivity, are presented. All in all, the intimate, fundamental correlation of the nanostructure (crystalline, chemical, magnetic…) to the physical properties of the nanoparticles is ascertained.