Nanoscience and its associated nanotechnology started several decades ago to discover and harness properties and behavior of materials that occur due to lowering their dimensionality. Nanomagnetism, which is the branch of nanoscience to investigate magnetic properties of materials down to fundamental length and time scales led to the discovery of a plethora of novel nanoscale spin phenomena and has further laid the groundwork for spintronics, which has become the primary enabler for the most advanced information technologies, including magnetic storage and sensor devices. So far, low-dimensional magnetic systems have been confined to zero (quantum dots), one (nanowires), and two (thin films) dimensions, however, recently research with artificially designed three-dimensional magnetic systems is emerging as it opens the path to novel scientifically exciting phenomena with enormous technological potential to advance spintronics further towards ultrasmall, ultrafast and most importantly low-power electronics. These three-dimensional structures harness the scientific achievements from traditional nanomagnetism, but expand them in a tailored way into the third dimension. Local curvature, particular when defined in a rather broad sense, including geometrical curvature adds to a traditional 2D film a third dimension and proximity effects drawing upon the 3D environment are among the design principles for those 3D magnetic systems. This critical focus article reviews briefly the current state-of-the-art of the emerging research topic with 3D nanomagnetic materials, and describes some of the challenges that the research community needs to address in terms of synthesis and fabrication, theory and modelling, as well as characterization and validation to ultimately bring to bear potential applications with 3D nanomagnetic devices.