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Research in presentation attack detection (PAD) for iris recognition has largely moved beyond evaluation in "closed-set" scenarios, to emphasize ability to generalize to presentation attack types not present in the training data. This paper offers several contributions to understand and extend the state-of-the-art in open-set iris PAD. First, it describes the most authoritative evaluation to date of iris PAD. We have curated the largest publicly-available image dataset for this problem, drawing from 26 benchmarks previously released by various groups, and adding 150,000 images being released with the journal version of this paper, to create a set of 450,000 images representing authentic iris and seven types of presentation attack instrument (PAI). We formulate a leave-one-PAI-out evaluation protocol, and show that even the best algorithms in the closed-set evaluations exhibit catastrophic failures on multiple attack types in the open-set scenario. This includes algorithms performing well in the most recent LivDet-Iris 2020 competition, which may come from the fact that the LivDet-Iris protocol emphasizes sequestered images rather than unseen attack types. Second, we evaluate the accuracy of five open-source iris presentation attack algorithms available today, one of which is newly-proposed in this paper, and build an ensemble method that beats the winner of the LivDet-Iris 2020 by a substantial margin. This paper demonstrates that closed-set iris PAD, when all PAIs are known during training, is a solved problem, with multiple algorithms showing very high accuracy, while open-set iris PAD, when evaluated correctly, is far from being solved. The newly-created dataset, new open-source algorithms, and evaluation protocol, made publicly available with the journal version of this paper, provide the experimental artifacts that researchers can use to measure progress on this important problem.