Networks are often modeled by random processes in which nodes are added one-by-one, according to some simple random rule. Uniform and preferential attachment trees are among the simplest examples of such dynamically growing networks. The statistical problems we address in this talk regard discovering the past of the tree when a present-day snapshot is observed. We present results that show that, even in gigantic networks, a lot of information is preserved from the early days. In particular, we discuss the problem of finding the root and the broadcasting problem.