Complex systems consist of many interacting components. Understanding the connections between these components is critical for evaluating the system's stability and for predicting its future state. Such systems can be represented by a network, with nodes denoting the individual participants and edges indicating associations between members. In this dissertation, we explore methods of learning financial and biological networks. We begin by estimating networks of large financial institutions, applying pairwise and system-wide Granger causality methods to time series of the firms' monthly stock returns. We consider both mean-based Granger causality as well as a tail-based version that relies on quantile regression, from which we can distinguish interfirm connections that exist during different market conditions. Next, we build upon these ideas by constructing financial networks from high-frequency (intraday) trade data using machine learning techniques. In both the low- and high-frequency settings, we demonstrate how the networks can be used to detect critical economic events, ex post, and to identify important financial institutions. Finally, we use partial correlation and debiased graphical Lasso to estimate a network of genes based on their essentiality profiles. This network can be used to identify groups of interacting genes that may be promising candidates for further experimental validation.