  Modellers of large scale genome rearrangement events, in which segments of
DNA are inverted, moved, swapped, or even inserted or deleted, have found a
natural syntax in the language of permutations. Despite this, there has been a
wide range of modelling choices, assumptions and interpretations that make
navigating the literature a significant challenge. Indeed, even authors of
papers that use permutations to model genome rearrangement can struggle to
interpret each others' work, because of subtle differences in basic assumptions
that are often deeply ingrained (and consequently sometimes not even
mentioned). In this paper, we describe the different ways in which permutations
have been used to model genomes and genome rearrangement events, presenting
some features and limitations of each approach, and show how the various models
are related. This paper will help researchers navigate the landscape of genome
rearrangement models, and make it easier for authors to present clear and
consistent models.
