This paper presents a systematic literature review of state-of-the-art user experience (UX) frameworks for human-centered AI (HCAI) in generative AI systems. Seventeen key publications were analyzed to evaluate their contributions and identify research gaps based on established theoretical and practical principles. The findings highlight significant advancements in defining framework goals, integrating holistic user experiences, and emphasizing ethical principles, participatory design, and interdisciplinary collaboration. However, critical gaps persist, including a lack of standardized evaluation criteria, insufficient empirical validation, limited focus on adaptivity and iterative design, and underrepresentation of trust and control mechanisms. These challenges hinder the scalability and practical application of current frameworks. To address these issues, the study synthesizes best practices and proposes actionable opportunities, such as enhancing iterative design, fostering trust-building mechanisms, and promoting adaptivity and context-aware design. This review lays the foundation for advancing robust, user-centered, and ethically grounded UX frameworks to support the effective development of generative AI systems.