This thesis examines methods of doing inference with high-dimensional time series data. High-dimensional data – or “Big Data” – has a large number of different variables, which may greatly exceed the number of observations we have for each variable. While such data can be rich in information, classical statistical methods typically perform poorly in this setting. The work focuses on new methods designed to deal with this challenge, and specifically examine their properties with time series data, where observations depend on each other over time. While the main contributions are theoretical in nature, the thesis includes a variety of simulation studies, uses the methods in empirical applications, and a software package was created which implements these methods in a user-friendly way.