Generative Artificial Intelligence (GenAI) tools have become increasingly prevalent in software development, offering assistance to various managerial and technical project activities. Notable examples of these tools include OpenAIs ChatGPT, GitHub Copilot, and Amazon CodeWhisperer. Although many recent publications have explored and evaluated the application of GenAI, a comprehensive understanding of the current development, applications, limitations, and open challenges remains unclear to many. Particularly, we do not have an overall picture of the current state of GenAI technology in practical software engineering usage scenarios. We conducted a literature review and focus groups for a duration of five months to develop a research agenda on GenAI for Software Engineering. We identified 78 open Research Questions (RQs) in 11 areas of Software Engineering. Our results show that it is possible to explore the adoption of GenAI in partial automation and support decision-making in all software development activities. While the current literature is skewed toward software implementation, quality assurance and software maintenance, other areas, such as requirements engineering, software design, and software engineering education, would need further research attention. Common considerations when implementing GenAI include industry-level assessment, dependability and accuracy, data accessibility, transparency, and sustainability aspects associated with the technology. GenAI is bringing significant changes to the field of software engineering. Nevertheless, the state of research on the topic still remains immature. We believe that this research agenda holds significance and practical value for informing both researchers and practitioners about current applications and guiding future research.