  In this paper we review various models of curvature singularity free black
holes. In the first part of the review we describe semi-classical solutions of
the Einstein equations which, however, contains a "quantum" input through the
matter source. We start by reviewing the early model by Bardeen where the
metric is regularized by-hand through a short-distance cut-off, which is
justified in terms of non-linear electro-dynamical effects. This a toy-model
model useful to point-out the common features shared by all regular
semi-classical black holes. Then, we solve Einstein equations with a Gaussian
source encoding the quantum spread of an elementary particle. We identify, the
a priori arbitrary, Gaussian width with the Compton wavelength of the quantum
particle. This Compton-Gauss model leads to the estimate of a terminal density
that a gravitationally collapsed object can achieve. We identify this density
to be the Planck density, and reformulate the Gaussian model assuming this as
its peak density. All these models, are physically reliable as long as the
black hole mass is big enough with respect to the Planck mass. In the truly
Planckian regime, the semi-classical approximation breaks down. In this case, a
fully quantum black hole description is needed. In the last part of this paper,
we propose a non-geometrical quantum model of Planckian black hole implementing
the Holographic Principle and realizing the "classicalization" scenario
recently introduced by Dvali and collaborators. The classical relation between
the mass and radius of the black hole emerges only in the classical limit, far
away from the Planck scale.
