In this talk, I will describe an approach to the problem of gauge choice for the Yang-Mills equations on the (d+1)-dimensional Minkowski space ($d \geq 2$), which reveals the special structure (e.g. null structure) of the equations and is applicable to arbitrarily large data. The key ingredient is the Yang-Mills heat flow, which is a parabolic analogue of the Yang-Mills equations. Several applications of this approach will be described, including an alternative proof of the finite energy global well-posedness in $d=3$ (a classical result of Klainerman-Machedon '95) and a proof of almost optimal local well-posedness in $d=4$ for arbitrarily large data.