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While Vision-Language Models (VLMs) have achieved competitive performance in various tasks, their comprehension of the underlying structure and semantics of a scene remains understudied. To investigate the understanding of VLMs, we study their capability regarding object properties and relations in a controlled and interpretable manner. To this scope, we introduce CIVET, a novel and extensible framework for systemati**C** evaluat**I**on **V**ia controll**E**d s**T**imuli. CIVET addresses the lack of standardized systematic evaluation for assessing VLMs’ understanding, enabling researchers to test hypotheses with statistical rigor. With CIVET, we evaluate five state-of-the-art VLMs on exhaustive sets of stimuli, free from annotation noise, dataset-specific biases, and uncontrolled scene complexity. Our findings reveal that 1) current VLMs can accurately recognize only a limited set of basic object properties; 2) their performance heavily depends on the position of the object in the scene; 3) they struggle to understand basic relations among objects. Furthermore, a comparative evaluation with human annotators reveals that VLMs still fall short of achieving human-level accuracy.