Nanotechnology reduces the sizes of devices to a scale of hundreds of nanometres. The integration of such nano-sized entities equipped with fundamental functional units enables the development of nanosensors. These offer the prospect of the development of new tools to discover novel events at the nanoscale. To enlarge the capabilities of individual nanosensors, a number of them can be interconnected to establish nanosensor based networks, namely nanonetworks. These will empower new applications in many fields, such as healthcare, military, and environmental monitoring, and so on. The miniatured size of nanoantennas and their properties lead to communications within nanonetworks within the Terahertz (THz) band (0.1 - 10 THz). The objective of this thesis is to improve the system performance of graphene-enabled EM nanonetworks in this THz Band. Firstly, the channel model for THz waves is studied, and the path loss, channel noise and channel capacity for the THz band are analysed. Secondly, a novel three-terminal relaying protocol for nanonetworks is proposed and its performance is numerically investigated. Both amplify-and-forward (AF) and decode-and-forward (DF) relaying modes are studied. Thirdly, a new nano-rectenna based energy harvesting system is developed to power nanosensors within nanonetworks. The results obtained indicate the great potential and advantage of nano-rectennas. Fourthly, a simultaneous wireless information and power transfer system for nanonetworks in the THz Band is proposed. An amplify and forward (AF) relaying nanonetwork in this band is investigated. The performance of the system based on both time-switching and power-splitting protocols is numerically analysed.