The field of functional neuroimaging has substantially advanced as a big data science in the past decade, thanks to intational collaborative projects and community efforts. Here we conducted a literature review on functional neuroimaging, with focus on three general challenges in big data tasks: data collection and sharing, data infrastructure construction, and data analysis methods. The review covers a wide range of literature types including perspectives, database descriptions, methodology developments, and technical details. We show how each of the challenges was proposed and addressed, and how these solutions formed the three core foundations for the functional neuroimaging as a big data science and helped to build the current data-rich and data-driven community. Furthermore, based on our review of recent literature on the upcoming challenges and opportunities toward future scientific discoveries, we envisioned that the functional neuroimaging community needs to advance from the current foundations to better data integration infrastructure, methodology development toward improved leing capability, and multi-discipline translational research framework for this new era of big data.