Quantum gravity is the missing piece in our understanding of the fundamental
interactions today. Given recent observational breakthroughs in gravity,
providing a quantum theory for what lies beyond general relativity is more
urgent than ever. However, the complex history of quantum gravity and the
multitude of available approaches can make it difficult to get a grasp of the
topic and its main challenges and opportunities. We provide a guided tour of
quantum gravity in the form of 30 questions, aimed at a mixed audience of
learners and practitioners. The issues covered range from basic motivational
and background material to a critical assessment of the status quo and future
of the subject. The emphasis is on structural issues and our current
understanding of quantum gravity as a quantum field theory of dynamical
geometry beyond perturbation theory. We highlight the identification of quantum
observables and the development of effective numerical tools as critical to
future progress.
This article reviews the present status of the spin foam approach to the
quantization of gravity. Special attention is payed to the pedagogical
presentation of the recently introduced new models for four dimensional quantum
gravity. The models are motivated by a suitable implementation of the path
integral quantization of the Plebanski formulation of gravity on a simplicial
regularization. The article also includes a self-contained treatment of the 2+1
gravity. The simple nature of the latter provides the basis and a perspective
for the analysis of both conceptual and technical issues that remain open in
four dimensions.