  The emergence of local moments in graphene zigzag edges, grain boundaries,
vacancies and sp3 defects has been widely studied theoretically. However,
conclusive experimental evidence is scarce. Recent progress in on-surface
synthesis has made it possible to create nanographenes, such as triangulenes,
with local moments in their ground states, and to probe them using scanning
tunnelling microscope (STM) spectroscopy. Here we review the application of the
theory of sequential and cotunneling transport to relate the dI/dV spectra with
the spin properties of nanographenes probed by STM. This approach permits us to
connect the dI/dV with the many-body energies and wavefunctions of the graphene
nanostructures. We apply this method describing the electronic states of the
nanographenes by means of exact diagonalization of the Hubbard model within a
restricted Active Space. This permits us to provide a proper quantum
description of the emergence of local moments in graphene and its interplay
with transport. We discuss the results of this theory in the case of diradical
nanographenes, such as triangulene, rectangular ribbons and the Clar goblet,
that have been recently studied experimentally by means of STM spectroscopy.
This approach permits us to calculate both the dI/dV spectra, that yields
excitation energies, as well as the atomically resolved conductivity maps, that
provide information on the wavefunctions of the collective spin modes.
