Estimating network connectivity among multiple time series is an important problem in many areas of biological and social sciences. Examples include system-wide risk monitoring in financial economics and functional connectivity analysis in neuroscience. In this talk, I will present some recent works on building networks from multivariate time series data, where the core idea is to learn from lead-lag relationships between two time series in addition to their contemporaneous association. In the context of modeling networks of interactions among financial firms and measuring systemic risk, we will demonstrate how linear and quantile-based Granger causality analyses using vector autoregressive (VAR) models can provide insight. We will conclude with some model-free techniques for building networks among time series using multivariate spectral density and its inverse, and show their applications in functional connectivity analysis. Asymptotic theory of these methods under high-dimensional regime will be discussed.