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In open-world learning, an agent starts with a set of known classes, detects, and manages things that it does not know, and learns them over time from a non-stationary stream of data. Open-world learning is related to but also distinct from a multitude of other learning problems and this paper briefly analyzes the key differences between a wide range of problems including incremental learning, generalized novelty discovery, and generalized zero-shot learning. This paper formalizes various open-world learning problems including open-world learning without labels. These open-world problems can be addressed with modifications to known elements, we present a new framework that enables agents to combine various modules for novelty-detection, novelty-characterization, incremental learning, and instance management to learn new classes from a stream of unlabeled data in an unsupervised manner, survey how to adapt a few state-of-the-art techniques to fit the framework and use them to define seven baselines for performance on the open-world learning without labels problem. We then discuss open-world learning quality and analyze how that can improve instance management. We also discuss some of the general ambiguity issues that occur in open-world learning without labels.