Enhancing the fine-grained instance spatiotemporal motion perception capabilities of Video Large Language Models is crucial for improving their temporal and general video understanding. However, current models struggle to perceive detailed and complex instance motions. To address these challenges, we have made improvements from both data and model perspectives. In terms of data, we have meticulously curated iMOVE-IT, the first large-scale instance-motion-aware video instruction-tuning dataset. This dataset is enriched with comprehensive instance motion annotations and spatiotemporal mutual-supervision tasks, providing extensive training for the model's instance-motion-awareness. Building on this foundation, we introduce iMOVE, an instance-motion-aware video foundation model that utilizes Event-aware Spatiotemporal Efficient Modeling to retain informative instance spatiotemporal motion details while maintaining computational efficiency. It also incorporates Relative Spatiotemporal Position Tokens to ensure awareness of instance spatiotemporal positions. Evaluations indicate that iMOVE excels not only in video temporal understanding and general video understanding but also demonstrates significant advantages in long-term video understanding.