We will discuss the Firefighter model, that is a deterministic, discrete-time model of the spread of a fire on the vertices of a graph. In the Firefighter model, a fire erupts on some finite set X and in every time step all vertices adjacent to the fire catch fire as well (burning vertices continue to burn indefinitely) . At turn n we are allowed to protect f(n) vertices so that they never catch fire. We will discuss two different questions in this setting- the fire-containment problem and the fire-retainment problem. The classical firefighter problem, also known as the fire-containment problem, asks how large should f(n) be so that we will eventually contain any initial fire. The fire-retainment problem asks how large should f(n) be for saving only a ?sufficient? portion of the graph. We will be mainly interested in the asymptotic behaviour of f in relation with the geometry of the graph, focusing on Cayley graphs. The growth rates of these functions are nice quasi-isometric invariants of groups. We will discuss the results about these invariants for different classes of groups. This is a joint work with G. Amir, R. Baldasso and G.Kozma.