Emerging from the symbiotic combination of nanotechnology and communications, the field of nanonetworking has come a long way since its inception more than fifteen years ago. Significant progress has been achieved in several key communication technologies as enablers of the paradigm, as well as in the multiple application areas that it opens. In this paper, the focus is placed on the electromagnetic nanonetworking paradigm, providing an overview of the advances made in wireless nanocommunication technology from microwave through terahertz to optical bands. The characteristics and potential of the compared technologies are then confronted with the requirements and challenges of the broad set of nanonetworking applications in the Internet of NanoThings (IoNT) and on-chip networks paradigms, including quantum computing applications for the first time. Finally, a selection of cross-cutting issues and possible directions for future work are given, aiming to guide researchers and practitioners towards the next generation of electromagnetic nanonetworks.