  We review recent progress in the understanding of the role of multiple- and
simultaneous multiple merger coalescents as models for the genealogy in
idealised and real populations with exceptional reproductive behaviour. In
particular, we discuss models with `skewed offspring distribution' (or under
other non-classical evolutionary forces) which lead in the single locus haploid
case to multiple merger coalescents, and in the multi-locus diploid case to
simultaneous multiple merger coalescents. Further, we discuss inference methods
under the infinitely-many sites model which allow both model selection and
estimation of model parameters under these coalescents.
