Integrating artificial intelligence (AI) with immersive analytics (IA) represents a promising means of leveraging advanced computational techniques to enhance data visualization and analysis. This study examines the state-of-the-art of AI-IA integration by addressing three key research issues: the significant application domains, the AI techniques used and their combinations, and current challenges and future directions. Results of reviewing 43 relevant studies reveal that AI-IA integration is still in its early stages, as existing research has mainly focused on a limited range of data types and application scenarios. By analyzing the application domains, this systematic literature review supports previous findings of important applications in the fields of education, manufacturing, and healthcare. At the same time, it identifies emerging applications that have progressed from XR and AI domains to AI-IA integration, such as sports events, assistive systems, urban planning, and disaster management. We contribute to extending established visual analytics (VA) pipelines into XR environments with integrated AI techniques. AI techniques are identified as contributing in five ways to this IA pipeline. Our contribution also includes identifying four key challenges and seven opportunities for future exploration. The review concludes that combining AI and IA holds the potential to create innovative applications using advanced AI and immersive visualization techniques. We present an overview of these applications and address key issues for future development.