A solution to the unnormalized Ricci flow equation is called immortal if it exists for all times $t > 0$. The asymptotic behavior of these solutions is in general much less understood than in the case of a finite time singularity. For instance, they might be collapsed, and they might also converge locally to non-gradient solitons, which cannot be detected using Perelman's entropy functional. In this talk, we will show that for immortal homogeneous solutions of arbitrary dimension and isometry group, the flow subconverges (after parabolic rescaling) to an expanding homogeneous Ricci soliton. We will also give further results in the special case of solvable Lie groups. This is joint work with Christoph Bohm.