Network science provides theoretical, computational, and empirical tools that can be used to understand the structure and function of the human brain in novel ways using simple concepts and mathematical representations. Network neuroscience is a rapidly growing field that is providing considerable insight into human structural connectivity, functional connectivity while at rest, changes in functional networks over time (dynamics), and how these properties differ in clinical populations. In addition, a number of studies have begun to quantify network characteristics in a variety of cognitive processes and provide a context for understanding cognition from a network perspective. In this review, we outline the contributions of network science to cognitive neuroscience. We describe the methodology of network science as applied to the particular case of neuroimaging data and review its uses in investigating a range of cognitive functions including sensory processing, language, emotion, attention, cognitive control, learning, and memory. In conclusion, we discuss current frontiers and the specific challenges that must be overcome to integrate these complementary disciplines of network science and cognitive neuroscience. Increased communication between cognitive neuroscientists and network scientists could lead to significant discoveries under an emerging scientific intersection known as cognitive network neuroscience.