AI systems are not only becoming better in solving complex reasoning challenges, but also in performing creative tasks. One of the creative tasks where AI systems still struggle to achieve human performance, however, is humor processing, for which mixed results have been reported. Therefore, the goal of this survey is to categorize recent research in computational humor modeling in order to identify current trends, advancements, and remaining gaps. The scope of this work is broader than previous survey papers, as we tackle not only text-based models, but also multimodal models, and discuss a variety of detection and generation tasks.