Several standard stochastic PDEs (SPDEs) from physics are not well-posed due to the presence of undefined products when one tries to compute them. In 2013, Martin Hairer developed the theory of regularity structures to give a notion of solution to all of those SPDEs that are “subcritical” and was subsequently awarded the Fields Medal the following year. The idea behind the theory of regularity structure is to introduce an abstract space where one may make sense of previously undefined terms, and then connect this abstract space with the physical space using two functions. In practice, this procedure corresponds to adding new “renormalization” terms in the stochastic PDE. The goal of this presentation is to provide an introduction to these different concepts.