  We review two works arXiv:2006.04987 and arXiv:2201.03487 which study the
stochastic quantisation equations of Yang-Mills on two and three dimensional
Euclidean space with finite volume. The main result of these works is that one
can renormalise the 2D and 3D stochastic Yang-Mills heat flow so that the
dynamic becomes gauge covariant in law. Furthermore, there is a state space of
distributional $1$-forms $\mathcal{S}$ to which gauge equivalence $\sim$
extends and such that the renormalised stochastic Yang-Mills heat flow projects
to a Markov process on the quotient space of gauge orbits $\mathcal{S}/{\sim}$.
In this review, we give unified statements of the main results of these works,
highlight differences in the methods, and point out a number of open problems.
