Superparamagnetic iron oxide nanoparticles (NPs) are used in a rapidly expanding number of research and practical applications in the biomedical field, including magnetic cell labeling separation and tracking, for therapeutic purposes in hyperthermia and drug delivery, and for diagnostic purposes, e.g., as contrast agents for magnetic resonance imaging. These applications require good NP stability at physiological conditions, close control over NP size and controlled surface presentation of functionalities. This review is focused on different aspects of the stability of superparamagnetic iron oxide NPs, from its practical definition to its implementation by molecular design of the dispersant shell around the iron oxide core and further on to its influence on the magnetic properties of the superparamagnetic iron oxide NPs. Special attention is given to the selection of molecular anchors for the dispersant shell, because of their importance to ensure colloidal and functional stability of sterically stabilized superparamagnetic iron oxide NPs. We further detail how dispersants have been optimized to gain close control over iron oxide NP stability, size and functionalities by independently considering the influences of anchors and the attached sterically repulsive polymer brushes. A critical evaluation of different strategies to stabilize and functionalize core–shell superparamagnetic iron oxide NPs as well as a brief introduction to characterization methods to compare those strategies is given.