  This Editorial introduces the Special Issue "Progress in Group Field Theory
and Related Quantum Gravity Formalisms" which includes a number of research and
review articles covering results in the group field theory (GFT) formalism for
quantum gravity and in various neighbouring areas of quantum gravity research.
We give a brief overview of the basic ideas of the GFT formalism, list some of
its connections to other fields, and then summarise all contributions to the
Special Issue.
