Efficient and accurate requirement specification for software development projects is crucial for a company's success. Generative AI has the potential to support the RE process in software development. This study examines the state-of-the-art of generative AI applications in RE through a systematic literature review. A combination of the methodology by Brocke and the forward and backward search approach by Webster and Watson was applied. The identified 37 relevant publications were analysed using a concept matrix based on Webster and Watson. The results indicate that generative AI is particularly useful in requirement elicitation, analysis, and specification, whereas requirement validation and industrial applications remain underexplored. The main challenges arise from ethical, data privacy, and practical implementation issues. The study highlights a research gap concerning the practical adoption of generative AI in industrial RE processes.