The reconstruction of species phylogenies from genomic data is a key step in modern evolutionary studies. This task is complicated by the fact that genes evolve under biological phenomena that produce discordant histories. These include hybrid speciation, horizontal gene transfer, gene duplication and loss, and incomplete lineage sorting, all of which can be modeled using random gene tree distributions building on well-studied discrete stochastic processes (branching processes, the coalescent, random rearrangements, etc.). Gene trees are in turn estimated from molecular sequences using Markov models on trees. The rigorous analysis of the resulting complex models can help guide the design of new reconstruction methods with computational and statistical guarantees. I will illustrate the challenges and opportunities in this area via a few recent results. No evolutionary biology background will be assumed.