  Classical extreme value statistics consists of two fundamental approaches:
the block maxima (BM) method and the peak-over-threshold (POT) approach. It
seems to be general consensus among researchers in the field that the POT
method makes use of extreme observations more efficiently than the BM method.
We shed light on this discussion from three different perspectives. First,
based on recent theoretical results for the BM approach, we provide a
theoretical comparison in i.i.d.\ scenarios. We argue that the data generating
process may favour either one or the other approach. Second, if the underlying
data possesses serial dependence, we argue that the choice of a method should
be primarily guided by the ultimate statistical interest: for instance, POT is
preferable for quantile estimation, while BM is preferable for return level
estimation. Finally, we discuss the two approaches for multivariate
observations and identify various open ends for future research.
