This thesis presents the design of Brick, a graph-based metadata schema for buildings that captures the entities (“things”) in a building and the relationships between them. We demonstrate how Brick's extensible class hierarchy is able to define the sets of entities required by energy efficiency applications by using Brick to model a suite of real-world buildings. Applications execute against Brick models by querying them for the information they need to operate. Queries are expressed using Brick's relationships, which capture associations between entities such as composition, influence, measurement and location. Together, these features of Brick enable an expressive, standardized, digital representation of buildings. We demonstrate how the Brick schema is implemented with the RDF data model and how models of buildings are queried with the standard SPARQL query language. This informs an investigation of the systems requirements for the infrastructure storing models and processing queries against them, involving a description of the expected Brick workload and an evaluation of existing RDF/SPARQL technologies. We then design and implement a performant query processor -- HodDB -- that provides interactive-level query latencies (sub 100ms). We evaluate HodDB on a synthetic Brick workload and demonstrate how it is used to implement novel integrations of Brick with data analysis and control systems.