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Despite its promise, RFID technology presents numerous challenges, including incomplete data, lack of location and containment information, and very high volumes. In this work, we present a novel data inference and compression substrate over RFID streams to address these challenges. Our substrate employs a time-varying graph model to efficiently capture possible object locations and interobject relationships such as containment from raw RFID streams. It then employs a probabilistic algorithm to estimate the most likely location and containment for each object. By performing such online inference, it enables online compression that recognizes and removes redundant information from the output stream of this substrate. We have implemented a prototype of our inference and compression substrate and evaluated it using both real traces from a laboratory warehouse setup and synthetic traces emulating enterprise supply chains. Results of a detailed performance study show that our data inference techniques provide high accuracy while retaining efficiency over RFID data streams, and our compression algorithm yields significant reduction in output data volume.