Generative AI applications are increasingly being used at universities to support both teachers and students and to take on tasks in the areas of teaching support and administration. At the same time, AI applications require far-reaching adjustments to institutional strategies at universities, the development of suitable technical infrastructures, skills development and processes in teaching and learning in order to ensure successful collaboration between humans and AI. Such adjustments are met with very different conditions at universities and are handled and promoted to varying degrees in different areas of universities, at different types of universities and in different countries. A survey conducted by the [deleted for peer review purposes] in spring 2025 among all universities in German-speaking countries provides information on the current state of universities‘ engagement with the potential of generative AI systems. The AI-related findings of this survey are examined in more detail in this article with regard to the question of how human-AI collaboration in the field of learning and teaching can be organised for the benefit of universities.