Abstract: Recent advancements in large language models (LLMs) have significantly improved their ability to generate natural and contextually relevant text, enabling more human-like AI interactions. However, generating and understanding interactive human-like motion, where multiple individuals engage in coordinated movements, remains challenging due to the complexity of modeling these interactions. Additionally, a unified and versatile model is needed to handle diverse interactive scenarios, such as chat systems that dynamically adapt to user instructions and assigned roles.To address these challenges, we introduce VIM, the Versatile Interactive Motion-language model, which integrates both language and motion modalities to effectively understand, generate, and control interactive motions in multi-turn conversational contexts. Unlike previous studies that primarily focus on uni-directional tasks such as text-to-motion or motion-to-text, VIM employs a unified architecture capable of simultaneously understanding and generating both motion and text modalities.Given the absence of an appropriate dataset to support this task, we introduce Inter-MT$^2$, a large-scale instruction-tuning dataset containing 82.7K multi-turn interactive motion instructions, covering 153K interactive motion samples. Inter-MT$^2$ spans diverse instructional scenarios, including motion editing, question answering, and story generation, leveraging off-the-shelf large language models and motion diffusion models to construct a broad set of interactive motion instructions.We extensively evaluate the versatility of VIM across multiple interactive motion-related tasks, including motion-to-text, text-to-motion, reaction generation, motion editing, and reasoning about motion sequences. Notably, VIM is the first model capable of effectively addressing all these tasks within a single unified framework, achieving competitive performance compared to task-specific methods.