  We propose seven criteria to single out physically reasonable non-singular
black-hole models and adopt them to four different spherically symmetric models
with a regular center and their rotating counterparts. In general relativity,
all such non-singular black holes are non-generic with a certain matter field
including a class of nonlinear electromagnetic fields. According to a criterion
that the effective energy-momentum tensor should satisfy all the standard
energy conditions in asymptotically flat regions, the well-known Bardeen and
Hayward black holes are discarded. In contrast, the Dymnikova and Fan-Wang
black holes respect the dominant energy condition everywhere. Although the
rotating Fan-Wang black hole contains a curvature singularity, the rotating
Dymnikova black hole is free from scalar polynomial curvature singularities and
closed timelike curves. In addition, the dominant energy condition is respected
on and outside the event horizons in the latter case. The absence of parallelly
propagated curvature singularities remains an open question.
