Is aesthetic impact different from beauty? Is visual salience a reflection of its capacity for effective communication? We present Impressions, a novel dataset through which to investigate the semiotics of images, and how specific visual features and design choices can elicit specific emotions, thoughts and beliefs. We posit that the impactfulness of an image extends beyond formal definitions of aesthetics, to its success as a communicative act, where style contributes as much to meaning formation as the subject matter. However, prior image captioning datasets are not designed to empower state-of-the-art architectures to model potential human impressions or interpretations of images. To fill this gap, we design an annotation task heavily inspired by image analysis techniques in the Visual Arts to collect 1,440 image-caption pairs and 4,320 unique annotations exploring impact, pragmatic image description, impressions, and aesthetic design choices. We show that existing multimodal image captioning and conditional generation models struggle to simulate plausible human responses to images. However, this dataset significantly improves their ability to model impressions and aesthetic evaluations of images through fine-tuning and few-shot adaptation.