Microfluidic systems are rapidly becoming commonplace tools for high-precision materials synthesis, biochemical sample preparation, and biophysical analysis. Typically, microfluidic systems are constructed in monolithic form by means of microfabrication and, increasingly, by additive techniques. These methods restrict the design and assembly of truly complex systems by placing unnecessary emphasis on complete functional integration of operational elements in a planar environment. Here, we present a solution based on discrete elements that liberates designers to build large-scale microfluidic systems in three dimensions that are modular, diverse, and predictable by simple network analysis techniques. We develop a sample library of standardized components and connectors manufactured using stereolithography. We predict and validate the flow characteristics of these individual components to design and construct a tunable concentration gradient generator with a scalable number of parallel outputs. We show that these systems are rapidly reconfigurable by constructing three variations of a device for generating monodisperse microdroplets in two distinct size regimes and in a high-throughput mode by simple replacement of emulsifier subcircuits. Finally, we demonstrate the capability for active process monitoring by constructing an optical sensing element for detecting water droplets in a fluorocarbon stream and quantifying their size and frequency. By moving away from large-scale integration toward standardized discrete elements, we demonstrate the potential to reduce the practice of designing and assembling complex 3D microfluidic circuits to a methodology comparable to that found in the electronics industry.