In joint work with Tim Perutz, we give a complete characterization of the exact Fukaya category of the punctured torus, denoted by Fuk(T_0). This, in particular, means that one can write down an explicit minimal model for Fuk(T_0) in the form of an A-infinity algebra, denoted by A, and classify A-infinity structures on the relevant algebra. A result that we will discuss is that no associative algebra is quasi-equivalent to the model A of the Fukaya category of the punctured torus, i.e. A is non-formal. We will then deduce that Fuk(T_0) is derived equivalent to the category of perfect complexes on an irreducible rational curve with a double point, an instance of homological mirror symmetry.