  Black holes are one of the most fascinating predictions of general
relativity. They are the natural product of the complete gravitational collapse
of matter and today we have a body of observational evidence supporting the
existence of black holes in the Universe. However, general relativity predicts
that at the center of black holes there are spacetime singularities, where
predictability is lost and standard physics breaks down. It is widely believed
that spacetime singularities are a symptom of the limitations of general
relativity and must be solved within a theory of quantum gravity. Since we do
not have yet any mature and reliable candidate for a quantum gravity theory,
researchers have studied toy-models of singularity-free black holes and of
singularity-free gravitational collapses in order to explore possible
implications of the yet unknown theory of quantum gravity. This book reviews
all main models of regular black holes and non-singular gravitational collapses
proposed in the literature, and discuss the theoretical and observational
implications of these scenarios.
