The study of the node profiles of random digital trees, which started in earnest in 2009 with a paper of H.-K. Hwang, P. Nicodeme, G. Park and W. Szpankowski, turned out to be a rich source of surprises and interesting phenomena. So far, we only have a complete understanding of the profiles of random tries (due to the above work). For the other two major classes of random digital trees, namely, random PATRICIA tries and random digital search trees, our knowledge is still incomplete. In this talk, I will survey previous results (including our recent results on the profiles of symmetric digital search trees) and explain what still has to be done.

Parts of this talk is based on joint work with M. Drmota (Vienna University of Technology), H.-K. Hwang (Academia Sinica) and R. Neininger (Goethe University).