A complete understanding of the brain requires an integrated description of the numerous scales of neural organization. It means studying the interplay of genes, synapses, and even whole brain regions which ultimately leads to different types of behavior, from perception to action, while asleep or awake. Yet, multiscale brain modeling is challenging, in part because of the difficulty to access simultaneously to information from multiple spatiotemporal scales. While some insights have been gained on the role of specific microcircuits (e.g., thalamocortical), a comprehensive characterization of how changes occurring at one scale can have an impact on other ones, remains poorly understood. Recent efforts to address this gap include the development of new analytical tools mostly adapted from network science and dynamical systems theory. These theoretical contributions provide a powerful framework to analyze and model interconnected complex systems exhibiting interactions within and between different scales, or layers. Here, we present recent advances for the characterization of the multiscale brain organization in terms of structure-function, oscillation frequencies and temporal evolution. Efforts are reviewed on the multilayer network properties underlying higher-order organization of neuronal assemblies, as well as on the identification of multimodal network-based biomarkers of brain pathologies, such as Alzheimer's disease. We conclude this Colloquium with a perspective discussion on how recent results from multilayer network theory, involving generative modeling, controllability and machine learning, could be adopted to address new questions in modern neuroscience.