Abstract. We discuss various types of exotic (non-standard) singularities in the Universe: a Big-Rip (BR or type I), a Sudden Future Singularity (SFS or type II), a Generalized Sudden Future Singularity, a Finite Scale Factor singularity (FSF or type III), a Big-Separation (BS or type IV) and a w-singularity. They are characterized by violation of all or some of the energy conditions which results in a blow-up of all or some of the physical quantities: the scale factor, the energy density, the pressure, and the barotropic index. We relate the emergence of these singularities with physical theories (superstring, brane, higher-order gravity, loop quantum cosmology). We show how the models involving exotic singularities may serve as dark energy by applying the observational data. In particular, we show that some of these exotic singularities (though being of a weak type according to relativistic definitions) may occur in the near future of the universe.