  This tutorial survey provides an overview of recent non-asymptotic advances
in statistical learning theory as relevant to control and system
identification. While there has been substantial progress across all areas of
control, the theory is most well-developed when it comes to linear system
identification and learning for the linear quadratic regulator, which are the
focus of this manuscript. From a theoretical perspective, much of the labor
underlying these advances has been in adapting tools from modern
high-dimensional statistics and learning theory. While highly relevant to
control theorists interested in integrating tools from machine learning, the
foundational material has not always been easily accessible. To remedy this, we
provide a self-contained presentation of the relevant material, outlining all
the key ideas and the technical machinery that underpin recent results. We also
present a number of open problems and future directions.
