  Following the observational evidence for cosmic acceleration which may
exclude a possibility for the universe to recollapse to a second singularity,
we review alternative scenarios of its future evolution. Although the de Sitter
asymptotic state is still an option, some other asymptotic states which allow
new types of singularities such as Big-Rip (due to a phantom matter) and sudden
future singularities are also admissible and are reviewed in detail. The
reality of these singularities which comes from the relation to observational
characteristics of the universe expansion are also revealed and widely
discussed.
