Labardini-Fragoso's classical construction allows to associate an ice quiver with potential to a bordered surface. The corresponding Higgs category (in the sense of Yilin Wu) categorifies the cluster algebra (with non invertible boundary coefficients) associated to the surface by Fomin--Shapiro--Thurston. In recent work, Merlin Christ has given a completely different description of this category as the "1-periodic topological Fukaya category". He obtains it by simplifying Haiden-Katzarkov-Kontsevich's construction of the topological Fukaya category associated with the surface. Our aim is to present Christ's construction and, if time permits, the ongoing project of extending it to cluster algebras appearing in higher Teichmuller theory.