This paper presents BigDAWG, a reference implementation of a new architecture for "Big Data" applications. Such applications not only call for large-scale analytics, but also for real-time streaming support, smaller analytics at interactive speeds, data visualization, and cross-storage-system queries. Guided by the principle that "one size does not fit all", we build on top of a variety of storage engines, each designed for a specialized use case. To illustrate the promise of this approach, we demonstrate its effectiveness on a hospital application using data from an intensive care unit (ICU). This complex application serves the needs of doctors and researchers and provides real-time support for streams of patient data. It showcases novel approaches for querying across multiple storage engines, data visualization, and scalable real-time analytics.