The advent of the Internet of Things (IoT) has given the opportunity for the optimization and realization of different applications in various areas. The implementation of the Internet of Nano-Things (IoNT) will revolutionize healthcare systems. It will streamline the diagnostic and prognostic processes and aid in the treatment of patients through accurate and localized drug delivery and tumor and disease detection. In this paper, we outline the different network models of IoNT and the architectural requirements for implementation. We highlight the main applications of IoNT and the significant challenges we face in implementing this technology in healthcare. We also discuss the communication and networking aspects of IoNT examining two paradigms; layer-based and non-layer based models including the comprised layers in the layered model. We finally provide a comparison between the two models and discuss the advantages, disadvantages of both.