The objective of this study is to investigate and to simulate the gaze deployment of observers on paintings. For that purpose, we built a large eye tracking dataset composed of 150 paintings belonging to 5 art movements. We observed that the gaze deployment over the proposed paintings was very similar to the gaze deployment over natural scenes. Therefore, we evaluate existing saliency models and propose a new one which significantly outperforms the most recent deep-based saliency models. Thanks to this new saliency model, we can predict very accurately what are the salient areas of a painting. This opens new avenues for many image-based applications such as animation of paintings or transformation of a still painting into a video clip.