In this work, we introduce a framework for creating, testing, versioning and archiving portable applications for analyzing neuroimaging data organized and described in compliance with the Brain Imaging Data Structure (BIDS). The portability of these applications (BIDS Apps) is achieved by using container technologies that encapsulate all binary and other dependencies in one convenient package. BIDS Apps run on all three major operating systems with no need for complex setup and configuration and thanks to the richness of the BIDS standard they require little manual user input. Previous containerized data processing solutions were limited to single user environments and not compatible with most multi tenant High Performance Computing systems. BIDS Apps overcome this limitation by taking advantage of the Singularity container technology. As a proof of concept, this work is accompanied by 18 ready to use BIDS Apps, packaging a diverse set of commonly used neuroimaging algorithms.