Three-dimensional (3D) cell culture technologies, such as organoids, are physiologically relevant models for basic and clinical applications. Automated microfluidics offers advantages in high-throughput and precision analysis of cells but is not yet compatible with organoids. Here, we present an automated, high-throughput, microfluidic 3D organoid culture and analysis system to facilitate preclinical research and personalized therapies. Our system provides combinatorial and dynamic drug treatments to hundreds of cultures and enables real-time analysis of organoids. We validate our system by performing individual, combinatorial, and sequential drug screens on human-derived pancreatic tumor organoids. We observe significant differences in the response of individual patient-based organoids to drug treatments and find that temporally-modified drug treatments can be more effective than constant-dose monotherapy or combination therapy in vitro. This integrated platform advances organoids models to screen and mirror real patient treatment courses with potential to facilitate treatment decisions for personalized therapy.