New distributions of mutational information are measurable thanks to single-cell sequencing technology. I first describe how some of these can be derived from a simple branching process model of neutral evolution and how some tools involved relate to the combinatorics of phylogenetic trees as well as of search trees in computer science. Using the neutral model as a baseline against which one can measure selection, I next consider emerging cancer cells acquiring deleterious antigenic mutations, triggering the immune system, which seeks to eliminate them. Informed by stochastic simulations, I then discuss what coevolutionary dynamics take place under different regimes of interactions between the immune cells and their cancer prey and how this can inform immunotherapeutic treatments. I close with ideas for how mathematical models of somatic evolution in cancer and in other organisms such as long-lived trees may learn from one another.