We briefly discuss non-singular black hole models, with the main focus on the
properties of non-singular evaporating black holes. Such black holes possess an
apparent horizon, however the event horizon may be absent. In such a case, the
information from the black hole interior may reach the external observer after
the complete evaporation of the black hole. This model might be used for the
resolution of the information loss puzzle. However, as we demonstrate, in a
general case the quantum radiation emitted from the black hole interior,
calculated in the given black hole background, is very large. This outburst of
the radiation is exponentially large for models with the redshift function
α=1. We show that it can be suppressed by including a non-trivial
redshift function. However, even this suppression is not enough to guarantee
self-consistency of the model. This problem is a manifestation of a general
problem, known as the "mass inflation". We briefly comment on possible ways to
overcome this problem in the models of non-singular evaporating black holes.Comment: 10 pages, Extended version of the plenary talk given at a Joint
Meeting: 13th International Conference on Gravitation, Astrophysics, and
Cosmology 15th Italian-Korean Symposium on Relativistic Astrophysics, Seoul,
July 03--07, 201
