Deepfake technologies have been blurring the boundaries between the real and unreal, likely resulting in malicious events. By leveraging newly emerged deepfake technologies, deepfake researchers have been making a great upending to create deepfake artworks (deeparts), which are further closing the gap between reality and fantasy. To address potentially appeared ethics questions, this paper establishes a deepart detection database (DDDB) that consists of a set of high-quality conventional art images (conarts) and five sets of deepart images generated by five state-of-the-art deepfake models. This database enables us to explore once-for-all deepart detection and continual deepart detection. For the two new problems, we suggest four benchmark evaluations and four families of solutions on the constructed DDDB. The comprehensive study demonstrates the effectiveness of the proposed solutions on the established benchmark dataset, which is capable of paving a way to more interesting directions of deepart detection. The constructed benchmark dataset and the source code will be made publicly available.