In recent years, the so-called network perspective has led to better understanding of the functioning of the brain in health and disease. The development of non-invasive imaging methods and the use of mathematical tools from graph theory allowed for investigating the structure and function of brain networks. Connections within structural networks can be reconstructed using diffusion magnetic resonance imaging, while functional imaging methods allow for investigating functional networks. The capabilities of the brain are based on network topology, which allows both functional segregation and integrative processing of information. This review represents an accessible introduction to the basic principles of graph theory and network neuroscience. We introduce measures of network topology and basic properties of human brain networks. We explain how neurological and psychiatric disorders affect the functioning of the brain as a network and illustrate the relevance of these findings for clinical practice. We also highlight some limitations of the network approach and future challenges to be addressed in this rapidly developing field of neuroscience.