Quantum Yang-Mills model is a type of quantum field theory with gauge symmetry. The rigorous construction of quantum Yang-Mills is a central problem in mathematical physics. Stochastic quantization formulates the problem as stochastic dynamics, which can be studied using tools from analysis, PDE and stochastic PDE. We will discuss stochastic quantization of Yang-Mills on the 2 and 3 dimensional tori. To this end we need to address a number of questions, such as the construction of a singular orbit space, together with a class gauge invariant observables (singular holonomies or Wilson loops), solving a stochastic PDE using regularity structures, and projecting the solution to the orbit space. Mostly based on joint work with Chandra, Chevyrev and Hairer.