This paper proposes a large-scale multi-modal dataset for referring motion expression video segmentation, focusing on segmenting and tracking target objects in videos based on language description of objects' motions. Existing referring video segmentation datasets often focus on salient objects and use language expressions rich in static attributes, potentially allowing the target object to be identified in a single frame. Such datasets underemphasize the role of motion in both videos and languages. To explore the feasibility of using motion expressions and motion reasoning clues for pixel-level video understanding, we introduce MeViS, a dataset containing 33,072 human-annotated motion expressions in both text and audio, covering 8,171 objects in 2,006 videos of complex scenarios. We benchmark 15 existing methods across 4 tasks supported by MeViS, including 6 referring video object segmentation (RVOS) methods, 3 audio-guided video object segmentation (AVOS) methods, 2 referring multi-object tracking (RMOT) methods, and 4 video captioning methods for the newly introduced referring motion expression generation (RMEG) task. The results demonstrate weaknesses and limitations of existing methods in addressing motion expression-guided video understanding. We further analyze the challenges and propose an approach LMPM++ for RVOS/AVOS/RMOT that achieves new state-of-the-art results. Our dataset provides a platform that facilitates the development of motion expression-guided video understanding algorithms in complex video scenes. The proposed MeViS dataset and the method's source code are publicly available at https://henghuiding.com/MeViS/