We recall the concept of a self-similar groupoid action $(G,E)$ on the path space of a finite graph.
We describe when the corresponding ample groupoid of germs $\mathcal G(G,E)$ is Hausdorff, minimal, effective and purely infinite.
Inspired by the work of Nekrashevych, we define the Higman-Thompson group $V_E(G)$ associated to $(G,E)$ using $G$-tables and relate it to the topological full group $[\![\mathcal G(G,E)]\!]$.
After recalling some concepts in groupoid homology, we discuss the Matui's AH-conjecture for $\mathcal G(G,E)$.