Vision-language models (VLMs) have rapidly evolved into general-purpose multimodal reasoners with strong zero-shot generalization. In this context, VLMs could greatly benefit the analysis of human gaze and attention, a central task in human behavior understanding that requires reasoning about the physical scene as well as the activity, interactions, and social context. However, the extent to which VLMs can reliably understand human gaze and related attentional behaviors remains largely unexplored. In this work, we present EyeVLM, a systematic evaluation framework for gaze understanding in VLMs across two complementary dimensions: tasks and models. To assess gaze understanding capabilities, we focus on two core tasks. The first, gaze following, i.e., predicting the 2D location where a person is looking, has a geometric and visual processing focus, requiring a precise understanding of the human face, attention direction, 3D scene structure, and spatial grounding of attended targets. The second, social gaze prediction, requires social and relational reasoning over multi-person interactions (e.g., mutual gaze and shared attention), and may benefit more from the LLM semantic reasoning capabilities within VLMs. Regarding models, EyeVLM evaluates these tasks in two ways: a zero-shot setting with a diverse set of state-of-the-art open- and closed-source VLMs, exploring different prompting strategies; and a fine-tuning approach based on task-specific QA pairs, studying the impact of model scale and data scale. As benchmarks, we rely on existing gaze understanding datasets and perform a systematic comparison with state-of-the-art purely visual models. Overall, our results show that current VLMs lack precise gaze understanding capabilities. While standard training helps reduce the gap with visual models, significant improvements are still needed.