maketitle Let $C$ be a symmetric generalized Cartan matrix, and $G$ the corresponding Kac-Moody group with Weyl group $W$. For $w\in W$ by definition, the subset $N^w:= N\cap B_- w B_-$ is a unipotent cell of $G$. We show that the coordinate ring $\CC[N^w]$ has a natural cluster algebra structure with the initial seed given by certain generalized minors. Each cluster provides a test for total positivity. We will review the necesary definitions in the $\mathsf{A}_n$-case, where everything comes down to basic notions from linear algebra. Then we proceed to sketch our proof of this result via categorification of the cluster algebra structure in terms of a stably 2-Calabi-Yau Frobenius subcategory $\mathcal{C}_w$ of the category of finite dimensional modules over the preprojective algebra $\Lam$ determined by $C$. As an extra benefit of this approach we obtain a ``dual semicanonical'' basis of $\CC[N^w]$ which contains all cluster monomials and a dual PBW-basis. A key role is played by certain generating functions for Euler characteristics of varieties of partial composition series.