The first half of the talk will be devoted to a general introduction to regularity structures. Then I will discuss the main results of the paper arxiv.org/abs/1902.02884 (by Bruned, Gabriel, Hairer and myself)on a class of stochastic PDEs whose solutions take values in a Riemannian manifold. This class of equations has a numberof interesting properties and is a case study of the scope of regularity structures.