The BRAIN Initiative aims to break new ground in the scale and speed of data collection in neuroscience, requiring tools to handle data in the magnitude of yottabytes (10(24)). The scale, investment and organization of it are being compared to the Human Genome Project (HGP), which has exemplified “big science” for biology. In line with the trend towards Big Data in genomic research, the promise of the BRAIN Initiative, as well as the European Human Brain Project, rests on the possibility to amass vast quantities of data to model the complex interactions between the brain and behavior and inform the diagnosis and prevention of neurological disorders and psychiatric disease. Advocates of this “data driven” paradigm in neuroscience argue that harnessing the large quantities of data generated across laboratories worldwide has numerous methodological, ethical and economic advantages, but it requires the neuroscience community to adopt a culture of data sharing and open access to benefit from them. In this article, we examine the rationale for data sharing among advocates and briefly exemplify these in terms of new “open neuroscience” projects. Then, drawing on the frequently invoked model of data sharing in genomics, we go on to demonstrate the complexities of data sharing, shedding light on the sociological and ethical challenges within the realms of institutions, researchers and participants, namely dilemmas around public/private interests in data, (lack of) motivation to share in the academic community, and potential loss of participant anonymity. Our paper serves to highlight some foreseeable tensions around data sharing relevant to the emergent “open neuroscience” movement.