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The paradigm of machine intelligence moves from purely supervised learning to a more practical scenario when many loosely related unlabeled data are available and labeled data is scarce. Most existing algorithms assume that the underlying task distribution is stationary. Here we consider a more realistic and challenging setting in that task distributions evolve over time. We name this problem as Semi-supervised meta-learning with Evolving Task diStributions, abbreviated as SETS. Two key challenges arise in this more realistic setting: (i) how to use unlabeled data in the presence of a large amount of unlabeled out-of-distribution (OOD) data; and (ii) how to prevent catastrophic forgetting on previously learned task distributions due to the task distribution shift. We propose an OOD Robust and knowleDge presErved semi-supeRvised meta-learning approach (ORDER), to tackle these two major challenges. Specifically, our ORDER introduces a novel mutual information regularization to robustify the model with unlabeled OOD data and adopts an optimal transport regularization to remember previously learned knowledge in feature space. In addition, we test our method on a very challenging dataset: SETS on large-scale non-stationary semi-supervised task distributions consisting of (at least) 72K tasks. With extensive experiments, we demonstrate the proposed ORDER alleviates forgetting on evolving task distributions and is more robust to OOD data than related strong baselines.