This paper explores how integrating artificial intelligence (AI) into integrated development environments (IDEs) is transforming software development, specifically how developers interact with their tools. This marks the emergence of a new field called human-AI experiences in IDEs (in-IDE HAX), exploring the dynamic evolution of human-computer interaction in AI-assisted coding environments. Through a systematic literature review of 90 studies, we analyze three aspects of AI-based IDE systems: impact, design, and quality. While AI-assisted coding improves developer productivity, it also poses challenges such as verification overhead and over-reliance. An effective interface must display context, provide explanations and transparency for suggestions, and support user control. We also address issues of correctness, maintainability, and security.