Network neuroscience investigates brain structure and function by using the tools of network science. In brain network models, structural connections between brain region pairs are modeled from diffusion-weighted imaging data, usually named structural connectome or structural connectivity. Functional connections are modeled from functional magnetic resonance imaging data by measuring temporal statistical dependencies between brain region pairs, usually known as functional connectivity or functional connectome. Examining several types of human brain connectivity data offers new insights on how the integration and segregation of information in the brain relates to human behavior, and how this organization may be altered in neurological diseases and disorders. However, this exploration has so far mainly been constrained to pairwise interactions, e.g. looking at brain networks as a set of dyadic relationships among regions. Beneficial because of its simplicity, this assumption severely limits the investigation of the complex dynamical processes arising from brain networks in health and disease. Here we try to overcome the aforementioned issue by proposing a new approach, rooted in recent advances in topological data analyses and simplicial complexes, and investigate the higher-order structural and functional organization of the brain. The overarching goal of this proposal is to explore macro-scale, time-dependent and disease-specific higher-order processes in human brain networks with the purpose of getting a deeper understanding of scenarios where brain dynamics is impaired or affected, as in the case of complex neurodegenerative diseases such as Alzheimer’s.