Raw data from the Chandra X-ray Observatory are processed by a set of standard data processing pipelines to create scientifically useful data products appropriate for further analysis by end users. Fully automated pipelines read the dumped raw telemetry byte stream from the spacecraft and perform the common reductions and calibrations necessary to remove spacecraft and instrumental signatures and convert the data into physically meaningful quantities that can be further analyzed by observers. The resulting data products are subject to automated validation to ensure correct pipeline processing and verify that the spacecraft configuration and scheduling matched the observers request and any constraints. In addition, pipeline processing monitors science and engineering data for anomalous indications and trending, and triggers alerts if appropriate. Data products are ingested and stored in the Chandra Data Archive, where they are made available for downloading by users. In this paper, we describe the architecture of the data processing system, including the scientific algorithms that are applied to the data, and interfaces to other subsystems. We place particular emphasis on the impacts of design choices on system integrity and maintainability. We review areas where algorithmic improvements or changes in instrument characteristics have required significant enhancements, and the mechanisms used to effect these changes while assuring continued scientific integrity and robustness. We discuss major enhancements to the data processing system that are currently being developed to automate production of the Chandra Source Catalog.