Magnetic nanoparticles (MNPs), and in particular iron oxide nanoparticles (mainly magnetite and maghemite), are being widely used in the form of aqueous colloids for biomedical applications. In such colloids, nanoparticles tend to form assemblies, either aggregates, if the union is permanent, or agglomerates, if it is reversible. These clustering processes have a strong impact on the MNPs' properties that are often not well understood. In this review, the causes and consequences of MNPs aggregation/agglomeration are reviewed and discussed. Special attention has been paid to the impact of the MNPs aggregation/agglomeration on their magnetic properties and heating properties, when exposed to an alternating magnetic field in the frame of magnetic hyperthermia. In addition, a model system with MNPs of two different sizes coated with three different molecules oleic acid, meso-2, 3-dimercaptosuccinic acid and poly(maleic anhydride-alt-1-octadecene) has been characterized and the results used to support the ideas reviewed.