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We give a concise overview of the theory of regularity structures as firstexposed in [Hai14]. In order to allow to focus on the conceptual aspects of thetheory, many proofs are omitted and statements are simplified. In order toprovide both motivation and focus, we concentrate on the study of solutions tothe stochastic quantisation equations for the Euclidean $\Phi^4_3$ quantumfield 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 naturallyas an idealised limiting object for several classes of smooth models.

Regularity structures and the dynamical $\Phi^4_3$ model