Nanotechnology is providing a new set of tools to the engineering community to design nanoscale components with unprecedented functionalities. The integration of several nano-components into a single entity will enable the development of advanced nanomachines. Nanonetworks, i.e., networks of nanomachines, will enable a plethora of applications in the biomedical, environmental, industrial and military fields. To date, it is still not clear how nanomachines will communicate. The miniaturization of a classical antenna to meet the size requirements of nanomachines would impose the use of very high radiation frequencies, which would compromise the feasibility of electromagnetic nanonetworks. Therefore, a new wireless technology is needed to enable this paradigm. The objective of this work is to establish the foundations of graphene-enabled electromagnetic communication in nanonetworks. First, novel graphene-based plasmonic nano-antennas are proposed, modeled and analyzed. The obtained results point to the Terahertz Band (0.1-10 THz) as the frequency range of operation of novel nanoantennas. For this, the second contribution in this work is the development of a novel channel model for Terahertz Band communication. In addition, the channel capacity of the Terahertz Band is numerically investigated to highlight the potential of this still-unregulated frequency band. Third, new communication mechanisms for electromagnetic nanonetworks are developed. These include a novel modulation based on the transmission of femtosecond-long pulses, new low-weight codes for channel error prevention in nanonetworks, a novel symbol detection scheme at the nano-receiver, a new energy model for self-powered nanomachines with piezoelectric nano-generators, and a new Medium Access Control protocol tailored to the Terahertz Band. Finally, a one-to-one nano-link is emulated to validate the proposed solutions.