What do random spanning trees, graph embeddings, random walks, simplices and graph curvature have in common? As you may have guessed from the title, they are indeed all intimately connected to the effective resistance on graphs! While originally invented as a tool to study electrical circuits, the effective resistance has proven time and again to be a graph characteristic with a variety of interesting and often surprising properties. Starting from a number of equivalent but complementary definitions of the effective resistance, we will take a stroll through some classical theorems (Rayleigh monotonicity, Foster's theorem), a few modern results (Klein's metricity, Fiedler's graph-simplex correspondence) and finally discuss number of recent developments (variance on graphs, discrete curvature and graph embeddings).