  We refer to the classic definition of a singularity in Einstein's general
relativity (based on geodesic incompletness) as well as to some other criteria
to evaluate the nature of singularities in cosmology. We review what different
(non-Big-Bang) types of singularities are possible even in the simplest
cosmological framework of Friedmann cosmology. We also show that various
cosmological singularities may be removed or changed due to the variability of
physical constants.
