Quantum gravity, higher derivatives and nonlocality

The aim of the workshop Quantum Gravity, Higher Derivatives & Nonlocality (QGRAV-2021) was to assess our current understanding of the interplay between gravity and quantum mechanics, with particular attention to what is the main role of higher derivatives and nonlocality in the formulation of a consistent theory of quantum gravity, and whether they are really necessary to describe Nature at a fundamental level. The workshop had brought together various schools of thought, and besides talks numerous discussions were also held. In addition to focusing on formal aspects of several approaches, applications of higher derivatives arid non locality were also discussed in the context of cosmology and black-hole physics. In this preface article we present a concise explanation of the main problems underlying the quantization of gravity in the high-energy regime, briefly list several approaches that have been proposed so far, and also provide a gist of what was intensively discussed during the workshop.