Automatic art analysis has been mostly focused on classifying artworks into different artistic styles. However, understanding an artistic representation involves more complex processes, such as identifying the elements in the scene or recognizing author influences. We present SemArt, a multi-modal dataset for semantic art understanding. SemArt is a collection of fine-art painting images in which each image is associated to a number of attributes and a textual artistic comment, such as those that appear in art catalogues or museum collections. To evaluate semantic art understanding, we envisage the Text2Art challenge, a multi-modal retrieval task where relevant paintings are retrieved according to an artistic text, and vice versa. We also propose several models for encoding visual and textual artistic representations into a common semantic space. Our best approach is able to find the correct image within the top 10 ranked images in the 45.5% of the test samples. Moreover, our models show remarkable levels of art understanding when compared against human evaluation.