  We give a concise overview of the theory of regularity structures as first
exposed in [Hai14]. In order to allow to focus on the conceptual aspects of the
theory, many proofs are omitted and statements are simplified. In order to
provide both motivation and focus, we concentrate on the study of solutions to
the stochastic quantisation equations for the Euclidean $\Phi^4_3$ quantum
field theory which can be obtained with the help of this theory. In particular,
we sketch the proofs of how one can show that this model arises quite naturally
as an idealised limiting object for several classes of smooth models.
