Context: Generative AI (GenAI) has emerged as a transformative tool in software engineering, with requirements engineering (RE) actively exploring its potential to revolutionize processes and outcomes. The integration of GenAI into RE presents both promising opportunities and significant challenges that necessitate systematic analysis and evaluation. Objective: This paper presents a comprehensive systematic literature review (SLR) analyzing state-of-the-art applications and innovative proposals leveraging GenAI in RE. It surveys studies focusing on the utilization of GenAI to enhance RE processes while identifying key challenges and opportunities in this rapidly evolving field. Method: A rigorous SLR methodology was used to analyze 27 carefully selected primary studies in-depth. The review examined research questions pertaining to the application of GenAI across various RE phases, the models and techniques used, and the challenges encountered in implementation and adoption. Results: The most salient findings include i) a predominant focus on the early stages of RE, particularly the elicitation and analysis of requirements, indicating potential for expansion into later phases; ii) the dominance of large language models, especially the GPT series, highlighting the need for diverse AI approaches; and iii) persistent challenges in domain-specific applications and the interpretability of AI-generated outputs, underscoring areas requiring further research and development. Conclusions: The results highlight the critical need for comprehensive evaluation frameworks, improved human-AI collaboration models, and thorough consideration of ethical implications in GenAI-assisted RE. Future research should prioritize extending GenAI applications across the entire RE lifecycle, enhancing domain-specific capabilities, and developing strategies for responsible AI integration in RE practices.