Deformations of path algebras of quivers with relations appear in various guises throughout algebra and geometry. I will explain how to give a complete and surprisingly workable description of their deformation theory via the combinatorics of reduction systems. This perspective has several advantages, for example it gives a straightforward method for computing Hochschild cohomology in degree 2 as first-order deformations of any suitable reduction system for the ideal of relations. It also provides tools to address the problem of finding an algebraization for certain formal deformations. This can be used to obtain convergent/strict quantizations of polynomial Poisson structures on R^d. This talk is based on https://arxiv.org/abs/2002.10001 joint with Zhengfang Wang and https://arxiv.org/abs/2201.03249 joint with Philipp Schmitt.