Neuroscience has made significant strides over the past decade in moving from a largely closed science characterized by anemic data sharing, to a largely open science where the amount of publicly available neuroscience data has increased dramatically. While this increase is driven in significant part by large prospective data sharing studies, we are starting to see increased sharing in the long tail of neuroscience data, driven no doubt by journal requirements and funder mandates. Concomitant with this shift to open is the increasing support of the FAIR data principles by neuroscience practices and infrastructure. FAIR is particularly critical for neuroscience with its multiplicity of data types, scales and model systems and the infrastructure that serves them. As envisioned from the early days of neuroinformatics, neuroscience is currently served by a globally distributed ecosystem of neuroscience-centric data repositories, largely specialized around data types. To make neuroscience data findable, accessible, interoperable, and reusable requires the coordination across different stakeholders, including the researchers who produce the data, data repositories who make it available, the aggregators and indexers who field search engines across the data, and community organizations who help to coordinate efforts and develop the community standards critical to FAIR. The International Neuroinformatics Coordinating Facility has led efforts to move neuroscience toward FAIR, fielding several resources to help researchers and repositories achieve FAIR. In this perspective, I provide an overview of the components and practices required to achieve FAIR in neuroscience and provide thoughts on the past, present and future of FAIR infrastructure for neuroscience, from the laboratory to the search engine.