Neuroscience is entering the era of `extreme data` with little experience and few plans for the associated volume, velocity, variety, and veracity challenges. This is a serious impediment for both the sharing of data across labs, as well as the utilization of modern and high-performance computing capabilities to enable data driven discovery. Here, we introduce BRAINformat, a novel file format and model for management and storage of neuroscience data. The BRAINformat library defines application-independent design concepts and modules that together create a general framework for standardization of scientific data. We describe the formal specification of scientific data standards, which facilitates sharing and verification of data and formats. We introduce the concept of Managed Objects, enabling semantic components of data formats to be specified as self-contained units, supporting modular and reusable design of data format components and file storage. The BRAINformat is built off of HDF5, enabling portable, scalable, and self-describing data storage. We introduce the novel concept of Relationship Attributes for modeling and use of semantic relationships between data objects, and discuss the annotation of data using dedicated data annotation modules provided by the BRAINformat library. Based on these concepts we implement dedicated, application-oriented modules and design a data standard for neuroscience data.The BRAINformat software library is open source, easy-to-use, and provides detailed user and developer documentation and is freely available at: https://bitbucket.org/oruebel/brainformat.