© 2020 Author(s). The scientific and technological exploration of three-dimensional magnetic nanostructures is an emerging research field that opens the path to exciting novel physical phenomena, originating from the increased complexity in spin textures, topology, and frustration in three dimensions. One can also anticipate a tremendous potential for novel applications with those systems in a magnetic sensor and information processing technologies in terms of improved energy efficiency, processing speed, functionalities, and miniaturization of future spintronic devices. These three-dimensional structures are distinct from traditional bulk systems as they harness the scientific achievements of nanomagnetism, which aimed at lowering the dimensions down to the atomic scale, but expand those now in a tailored and designed way into the third dimension. This research update provides an overview of the scientific challenges and recent progress with regard to advances in synthesis approaches and state-of-the-art nanoscale characterization techniques that are prerequisite to understand, realize, and control the properties, behavior, and functionalities of three-dimensional magnetic nanostructures.