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The appearance of an object can be fleeting when it transforms. As eggs are broken or paper is torn, their color, shape and texture can change dramatically, preserving virtually nothing of the original except for the identity itself. Yet, this important phenomenon is largely absent from existing video object segmentation (VOS) benchmarks. In this work, we close the gap by collecting a new dataset for Video Object Segmentation under Transformations (VOST). It consists of more than 700 high-resolution videos, captured in diverse environments, which are 21 seconds long on average and densely labeled with instance masks. A careful, multi-step approach is adopted to ensure that these videos focus on complex object transformations, capturing their full temporal extent. We then extensively evaluate state-of-the-art VOS methods and make a number of important discoveries. In particular, we show that existing methods struggle when applied to this novel task and that their main limitation lies in over-reliance on static appearance cues. This motivates us to propose a few modifications for the top-performing baseline that improve its capabilities by better modeling spatio-temporal information. But more broadly, the hope is to stimulate discussion on learning more robust video object representations.