Background: With the rising popularity of Artificial Intelligence (AI), there is a growing need to build large and complex AI-based systems in a cost-effective and manageable way. Like with traditional software, Technical Debt (TD) will emerge naturally over time in these systems, therefore leading to challenges and risks if not managed appropriately. The influence of data science and the stochastic nature of AI-based systems may also lead to new types of TD or antipatterns, which are not yet fully understood by researchers and practitioners. Objective: The goal of our study is to provide a clear overview and characterization of the types of TD (both established and new ones) that appear in AI-based systems, as well as the antipatterns and related solutions that have been proposed. Method: Following the process of a systematic mapping study, 21 primary studies are identified and analyzed. Results: Our results show that (i) established TD types, variations of them, and four new TD types (data, model, configuration, and ethics debt) are present in AI-based systems, (ii) 72 antipatterns are discussed in the literature, the majority related to data and model deficiencies, and (iii) 46 solutions have been proposed, either to address specific TD types, antipatterns, or TD in general. Conclusions: Our results can support AI professionals with reasoning about and communicating aspects of TD present in their systems. Additionally, they can serve as a foundation for future research to further our understanding of TD in AI-based systems.