Kingman's coalescent and its various ramifications are a standard tool
in population genetic modeling and also underlie many inference
procedures based on observed genetic variability in samples. However,
when variability of individual offspring numbers is extremely high,
which may for example be caused by demographic stochasticity in
combination with highly variable environments or by certain types of
selection, more general coalescents than Kingman's coalescent can
appear as the genealogy connecting a sample. Such coalescents allowing
multiple mergers, introduced in the mathematical literature
independently by J. Pitman, by S. Sagitov and by P. Donnelly and
T. Kurtz in 1999, are now being picked up in the biological literature
with a view towards explaining genetic variability in species where
the "classical" theory seems not to fit well, in particular various
marine species. They also pose their own statistical perspectives and
challenges. We discuss statistical inference methods and tests
pertaining to multiple merger coalescents and illustrate them using
simulated and some real datasets.