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Large Vision-Language Models (VLMs) have demonstrated strong capabilities in tasks requiring a fine-grained understanding of literal meaning in images and text, such as visual question-answering or visual entailment. However, there has been little exploration of the capabilities of these models when presented with images and captions containing figurative meaning, such as metaphors or humor. To close this gap, we propose a new task framing the figurative meaning understanding problem as an explainable visual entailment task, where the model has to predict whether the image (premise) entails a caption (hypothesis) and justify the predicted label with a textual explanation. The figurative phenomena can be present in the image, in the caption, or both. Using a human-AI collaboration approach, we build the accompanying expert-verified dataset V-FLUTE, containing 6,027 image, caption, label, explanation instances spanning five diverse figurative phenomena: metaphors, similes, idioms, sarcasm, and humor. Through automatic evaluation, we find that VLMs struggle to generalize from literal to figurative meaning, particularly when it is present in images. Further, we identify common types of errors in VLM reasoning (hallucination and incomplete or unsound reasoning) across classes of models via human evaluation.