The opportunity to explore the human connectome using cutting-edge neuroimaging methods has elicited widespread interest. How far will the field be able to progress in deciphering long-distance connectivity patterns and in relating differences in connectivity to phenotypic characteristics in health and disease? We discuss the daunting nature of this challenge in relation to specific complexities of brain circuitry and known limitations of in vivo imaging methods. We also discuss the excellent prospects for continuing improvements in data acquisition and analysis. Accordingly, we are optimistic that major insights will emerge from human connectomics in the coming decade.