Mean curvature flow is the negative gradient flow of the area functional, and it has attracted a lot of interest in the past few years. In this talk, we will discuss a PDE-based, gauge theoretic, construction of codimension-two mean curvature flows based on the Yang-Mills-Higgs functionals, a natural family of energies associated to sections and metric connections of Hermitian line bundles. The underlying idea is to approximate the flow by the solution of a parabolic system of equations and study the corresponding singular limit of these solutions as the scaling parameter goes to zero. This is based on joint work with A. Pigati and D. Stern.