In this article, we introduce the Push Tree problem, which exposes the tradeoffs between the use of push and pull mechanisms in information distribution systems. One of the interesting features of the Push Tree problem is that it provides a smooth transition between the minimum Steiner Tree and the Shortest Path problems. We present initial complexity results and analyze heuristics. Moreover, we discuss what lessons can be learned from the static and deterministic Push Tree problem for more realistic scenarios characterized by high uncertainty and changing information request and update patterns.