What does quantum gravity look like at or beyond the Planck scale?

I am reading an article called The fundamental nature of space and time by Gerard 't Hooft. On page 3 he writes the following:

Physically, however, the perturbative approach fails. The difficulty is not the fact that the finite parts of the counter terms can be freely chosen. The difficulty is a combination of two features: (i) perturbation expansion does not converge, and (ii) the expansion parameter becomes large if center-of-mass energies reach beyond the Planck value. The latter situation is very reminiscent of the old weak interaction theory where a quartic interaction was assumed among the fermionic fields. This Fermi theory was also “non-renormalizable”.

In the Fermi theory, this problem was solved: the theory was replaced by a Yang-Mills theory with Brout-Englert-Higgs mechanism. This was not just ‘a way to deal with the infinities’, it was actually an answer to an absolutely crucial question: what happens at small distance scales?. At small distance scales, we do not have quartic interactions among fermionic fields, we have a local gauge theory instead. This is actually also the superior way to phrase the problem of quantum gravity: What happens at, or beyond, the Planck scale?

My Question

Can someone explain in relatively laymens terms what we think happens with quantum gravity at or beyond the Planck scale?

I am not a layman persay but I am not at 't Hooft's level either. Something hitting an audience in between would be great.