The Landau-Ginzburg (LG) / Conformal Field Theory (CFT) correspondence predicts a relationship between certain categories of matrix factorisations (for the "LG potential'') and modular tensor categories (for the CFT side). This prediction has its origin in physics, and comes from observations about 2-dimensional $N=2$ supersymmetric quantum field theory. I will explain how this prediction is to be interpreted mathematically and what difficulties one encounters in doing this. After this I will discuss joint work with Ana Ros Camacho in which we realise the LG/CFT correspondence for the potentials $x^d$. The main ingredient in this is an enriched category theoretic version of the classical Temperley-Lieb/Jones-Wenzl construction of the representation category of quantum $\operatorname{su}(2)$.