  Penrose's singularity theorem implies that if a trapped region forms in a
gravitational collapse, then a singularity must form as well within such
region. However, it is widely expected that singularities should be generically
avoided by quantum gravitational effects. Here we shall explore both the
minimum requirements to avoid singularities in a gravitational collapse as well
as discuss, without relying on a specific quantum gravity model, the possible
regular spacetimes associated to such regularization of the spacetime fabric.
In particular, we shall expose the intimate and quite subtle relationship
between regular black holes, black bounces and their corresponding horizonless
object limits. In doing so, we shall devote specific attention to those
critical (extremal) black hole configurations lying at the boundary between
horizonful and horizonless geometries. While these studies are carried out in
stationary configurations, the presence of generic instabilities strongly
suggest the need for considering more realistic time-dependent dynamical
spacetimes. Missing specific dynamical models, much less rigorous statements
can be made for evolving geometries. We shall nonetheless summarize here their
present understanding and discuss their implications for future
phenomenological studies.
