Artificial intelligence (AI) permeates all fields of life, which resulted in new challenges in requirements engineering for artificial intelligence (RE4AI), e.g., the difficulty in specifying and validating requirements for AI or considering new quality requirements due to emerging ethical implications. It is currently unclear if existing RE methods are sufficient or if new ones are needed to address these challenges. Therefore, our goal is to provide a comprehensive overview of RE4AI to researchers and practitioners. What has been achieved so far, i.e., what practices are available, and what research gaps and challenges still need to be addressed? To achieve this, we conducted a systematic mapping study combining query string search and extensive snowballing. The extracted data was aggregated, and results were synthesized using thematic analysis. Our selection process led to the inclusion of 126 primary studies. Existing RE4AI research focuses mainly on requirements analysis and elicitation, with most practices applied in these areas. Furthermore, we identified requirements specification, explainability, and the gap between machine learning engineers and end-users as the most prevalent challenges, along with a few others. Additionally, we proposed seven potential research directions to address these challenges. Practitioners can use our results to identify and select suitable RE methods for working on their AI-based systems, while researchers can build on the identified gaps and research directions to push the field forward.