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Dark matter (DM) composed of very light scalar fields (axion-like particles, or ALPs) generically exhibits wave-like density fluctuations which are absent in models of heavier candidates. Rare transits of very overdense patches of axion DM through Earth can occur, giving rise to strong and exotic signals in terrestrial experiments. We explore the interesting possibility that large ALP density can be captured or trapped by the gravitational field of the Earth or Sun. In this talk, I will review both the case of transient boson star encounters with Earth, as well as miniature ALP halos captured in our solar system, and show how each might imply important modifications to the sensitivities of existing searches for light scalar fields.