The term “haplotype block” is commonly used in the developing field of
haplotype-based inference methods. We argue that the term should be
defined based on the structure of the Ancestral Recombination Graph
(ARG), which contains complete information on the ancestry of a sample.
We use simulated examples to demonstrate key features of the relation
between haplotype blocks and ancestral structure, emphasising the
stochasticity of the processes that generate them. Even the simplest
cases of neutrality or of a “hard” selective sweep produce a rich
structure, which is missed by commonly used statistics. We highlight a
number of novel methods for inferring haplotype structure as full ARG,
or as a sequence of trees. While some of these new methods are
computationally efficient, they still lack features to aid exploration
of the haplotype blocks, as we define them, thus calling for the
development of new methods. Understanding and applying the concept of
the haplotype block will be essential to fully exploit long and
linked-read sequencing technologies.