Real-world applications could benefit from the ability to automatically retarget an image to different aspect ratios and resolutions, while preserving its visually and semantically important content. However, not all images can be equally well processed that way. In this work, we introduce the notion of image retargetability to describe how well a particular image can be handled by content-aware image retargeting. We propose to learn a deep convolutional neural network to rank photo retargetability in which the relative ranking of photo retargetability is directly modeled in the loss function. Our model incorporates joint learning of meaningful photographic attributes and image content information which can help regularize the complicated retargetability rating problem. To train and analyze this model, we have collected a database which contains retargetability scores and meaningful image attributes assigned by six expert raters. Experiments demonstrate that our unified model can generate retargetability rankings that are highly consistent with human labels. To further validate our model, we show applications of image retargetability in retargeting method selection, retargeting method assessment and photo collage generation.