The emerging field of connectomics comprises extensive efforts to map patterns of brain connectivity, to represent these patterns with the tools of network science, and to explore the relation of brain connectivity and dynamics to behavior and cognition. Importantly, these efforts span multiple scales of brain organization, from synaptic connectivity among individual neurons, to comprehensive maps of circuits, neuronal populations, and projections among brain regions. An integrative multi-scale framework for mapping, analyzing and modeling connectome data sets is lacking. This Keystone Symposia meeting aims to narrow this important gap, by: 1) Fostering scientific exchange among otherwise siloed researchers studying connectomes in different organisms at different scales with different measurement techniques; 2) Promoting approaches that apply across scales, for example by leveraging the tools of network science; 3) Emphasizing the need to move beyond descriptive accounts of connectomes, to model-based prediction and control; 4) Providing a unique opportunity for pre- and postdoctoral trainees to engage with connectomics leaders and present their work. Anticipated outcomes include a multi-scale framework for description, prediction and control of connectomes; innovative computational methods for statistical analysis and modeling of connectome data sets; and new collaborations among participating researchers and trainees. The meeting will have transformative impact by creating new relationships among investigators and by seeding a new integrative research agenda centered on the structure and dynamics of brain connectivity.