Models for networks that evolve and change over time are ubiquitous in a host of domains including modeling social networks, understanding the evolution of systems in proteomics, the study of the growth and spread of epidemics etc.

This talk will give a brief summary of three recent findings in this area where stochastic approximation techniques play an important role:

1. Understanding the effect and detectability of change point in the evolution of the system dynamics.
2. Reconstructing the initial "seed" that gave rise to the current network, sometimes referred to as Network Archeology.
3. The disparity in the behavior of different centrality measures such as degree and page rank centrality for measuring popularity in settings where there are vertices of different types such as majorities and minorities as well as insight analyzing such problems give for at first sight unrelated issues such as sampling rare groups within the network.

The main goal will to be convey unexpected findings in each of these three areas and in particular the "unreasonable effectiveness" of continuous time branching processes.