  We provide a non-technical overview of recent extensions of renormalization
methods and techniques to Group Field Theories (GFTs), a class of
combinatorially non-local quantum field theories which generalize matrix models
to dimension $d \geq 3$. More precisely, we focus on GFTs with so-called
closure constraint, which are closely related to lattice gauge theories and
quantum gravity spin foam models. With the help of recent tensor model tools, a
rich landscape of renormalizable theories has been unravelled. We review our
current understanding of their renormalization group flows, at both
perturbative and non-perturbative levels.
