Quantum Gravity is a dream, a theoretical need and a scientific goal. It is a theory which still does not exist in complete form, but that many people claim to have had glimpses of, and it is an area of research which, at present, comprises the collective efforts of hundreds of theoretical and mathematical physicists.

This yet-to-be-found theory promises to be a more comprehensive and complete description of the gravitational interaction, a description that goes beyond Einstein's General Relativity in being possibly valid at all scales of distances and energy; at the same time it promises to provide a new and deeper understanding of the nature of space, time and matter.

As such, research in Quantum Gravity is a curious and exciting blend of rigorous mathematics and bold speculations, concrete models and general schemata, foundational questions and technical issues, together with, since recently, tentative phenomenological scenarios.

In the past three decades we have witnessed an amazing growth of the field of Quantum Gravity, of the number of people actively working in it, and consequently of the results achieved. This is due to the fact that some approaches to the problem started succeeding in solving outstanding technical challenges, in suggesting ways around conceptual issues, and in providing new physical insights and scenarios. A clear example is the explosion of research in string theory, one of the main candidates to a quantum theory of gravity, and much more.