Kadanoff's unversality hypothesis states that the critical phenomena of many systems undergoing (continuous) phase transitions depend only on essential macroscopic properties, such as lattice dimensions or intrinsic symmetries of the model. Lattice spin models form a rich playground to test the universality hypothesis. For one, they are mathematically tractable: the simplest example, the Ising model, has enjoyed an incredible amount of success over the years. Furthermore, their critical phenomena are expected to be governed by continuum objects called Euclidean quantum fields. In this talk, I'll give a gentle introduction to this landscape and an insight into what the big driving problems are.