Neuroimaging data analysis often requires purpose-built software, which can be challenging to install and may produce different results across computing environments. Beyond being a roadblock to neuroscientists, these issues of accessibility and portability can hamper the reproducibility of neuroimaging data analysis pipelines. Here, we introduce the Neurodesk platform, which harnesses software containers to support a comprehensive and growing suite of neuroimaging software (https://www.neurodesk.org/). Neurodesk includes a browser-accessible virtual desktop environment and a command line interface, mediating access to containerized neuroimaging software libraries on various computing platforms, including personal and high-performance computers, cloud computing and Jupyter Notebooks. This community-oriented, open-source platform enables a paradigm shift for neuroimaging data analysis, allowing for accessible, flexible, fully reproducible, and portable data analysis pipelines.