A Tropical QFT is a functor from a category of tropical curves up to type (as opposed to bordisms up to homotopy) to a linear category. Ruddat and I define this and construct a particular example whose target category consists of spaces of mirror polyvector fields. We show that this TrQFT elegantly computes the multiplicities which appear in tropical Gromov-Witten theory. I will sketch this and relate it to an expected isomorphism between a conjectural log/tropical quantum cohomology ring and the mirror ring of polyvector fields. In particular, I'll outline my proof of the degree 0 case of this for cluster varieties, a.k.a., the Frobenius structure conjecture, in which canonical ``theta functions" on cluster varieties are defined in terms of certain mirror logGW numbers. Finally, I'll discuss ideas on quantum and motivic refinements of this.