Despite the impressive progress of recent MLLMs on spatio-temporal video grounding (STVG), existing evaluations and training data focus primarily on simple queries. They largely overlook the compositional queries prevalent in real-world scenarios, where a target must be disambiguated by jointly reasoning about its attributes and relations to other entities. To bridge this gap, we propose Compositional Spatio-Temporal Video Grounding (CompSTVG), a task that requires models to process complex textual queries where every intertwined attribute and relational cue is essential for disambiguation. To facilitate this task at scale, we build a synthetic data engine that leverages a spatio-temporal scene graph as a difficulty measure and casts difficulty-controlled query synthesis as a constraint programming problem, producing difficulty-graded data for both evaluation and training. Built on this engine, we introduce STVG-CompBench, a benchmark stratified by explicit difficulty levels that jointly capture temporal complexity and spatial interference. Evaluating 11 representative STVG models on STVG-CompBench reveals that current models perform poorly on compositional queries, exhibiting a sharp performance drop that is typically obscured by overall dataset-level averages. We further construct synthetic training data and propose CurrSTVG, a curriculum reinforcement learning framework that delivers consistent gains, with the largest improvements observed on the most challenging compositional queries.

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