One of the key challenges in the current era of data science is the ubiquity of structured data, and one particularly prominent example of such data is network data. In this talk, I will illustrate how network versions of quite fundamental statistical problems yet remain to be addressed. Specifically, I will address the problems of (i) propagation of uncertainty to summary statistics of `noisy' networks, and (ii) estimation and testing for large collections of network data objects. In each case I will present a formalization of a certain class of problems encountered frequently in practice, describe our work in addressing the core aspects of these problems, and point to some of the many outstanding challenges remaining.