Cultural heritage data plays a key role in the understanding of past human history and culture, enriches the present and prepares the future. A wealth of information is buried in artwork images that can be extracted via digitization and analysis. While a huge number of methods exists, a deep review of the literature concerning object detection in visual art is still lacking. In this study, after reviewing several related papers, a comprehensive review is presented, including (i) an overview of major computer vision applications for visual art, (ii) a presentation of previous related surveys, (iii) a comprehensive overview of relevant object detection methods for artistic images. Considering the studied object detection methods, we propose a new taxonomy based on the supervision learning degree, the adopted framework, the adopted methodology (classical or deep-learning based method), the type of object to detect and the depictive style of the painting images. Then the several challenges for object detection in artistic images are described and the proposed ways of solving some encountered problems are discussed. In addition, available artwork datasets and metrics used for object detection performance evaluation are presented. Finally, we provide potential future directions to improve object detection performances in paintings.