The KPZ equation is a popular model of one-dimensional in-
terface propagation. From heuristic consideration, it is expected to be
"universal" in the sense that any "weakly asymmetric" or "weakly noisy"
microscopic model of interface propagation should converge to it if one
sends the asymmetry (resp. noise) to zero and simultaneously looks at the
interface at a suitable large scale. The only microscopic models for which
this has been proven so far all exhibit very particular that allow to perform
a microscopic equivalent to the Cole-Hopf transform. The main bottleneck
for generalisations to larger classes of models was that until recently it was
not even clear what it actually means to solve the equation, other than via
the Cole-Hopf transform. In this talk, we will see that there exists a rather
large class of continuous models of interface propagation for which conver-
gence to KPZ can be proven rigorously. The main tool for both the proof
of convergence and the identication of the limit is the recently developed
theory of regularity structures, but with an interesting twist.