The 2D XY model has attracted the attention of physicists and mathematicians for several decades. One way to understand this model is through its dual height function. Recent developments make it possible to show that the phase transition of the two models coincides. At the core of the proof is a new perspective on the Symanzik/Brydges – Fröhlich-Spencer random walk. The talk is based on arXiv:2301.06905 and arXiv:2211.14365.