This book presents different approaches to a rigorous unified description of quantum fields and gravity. It contains a carefully selected cross-section of lively discussions which took place in autumn 2010 at the fifth conference "Quantum field theory and gravity - Conceptual and mathematical advances in the search for a unified framework" in Regensburg, Germany. In the tradition of the other proceedings covering this series of conferences, a special feature of this book is the exposition of a wide variety of approaches, with the intention to facilitate a comparison. The book is mainly addressed to mathematicians and physicists who are interested in fundamental questions of mathematical physics. It allows the reader to obtain a broad and up-to-date overview of a fascinating active research area.