If we are to think critically about Big Data initiatives, we must learn to take them apart. This paper explains how to interrogate Big Data, not as large homogenous resources, but as heterogeneous collections with varied and discordant local ties. My argument focuses on the Big Data of media collections: composite digital repositories of texts, images, and video created in different contexts, but brought together online. The primary example used in this paper is the Digital Public Library of America (DPLA), a collection composed of digitized library, museum and archive records from institutions across the United States. I demonstrate how local readings of DPLA data can uncover schemata, errors, infrastructures, classifications, absences, and rituals that have important origins. Moreover, I explain how identifying these local features can support new forms of scholarship, pedagogy, and advocacy in the face of Big Data. For this last point, I use two additional cases: NewsScape, a real-time archive of broadcast news, and Zillow, a marketplace for real estate listings. The range of examples demonstrates how the stakes change from one Big Data initiative to the next. The paper concludes with a set of speculative guidelines for attending to the local conditions in Big Data: get dirty, take a comparative approach, show context, use data to connect people, and create opportunities for the collection of counter-data. When working with Big Data, I argue that thinking locally is thinking critically.