  The Euler characteristic transform (ECT) is a simple to define yet powerful
representation of shape. The idea is to encode an embedded shape using
sub-level sets of a a function defined based on a given direction, and then
returning the Euler characteristics of these sublevel sets. Because the ECT has
been shown to be injective on the space of embedded simplicial complexes, it
has been used for applications spanning a range of disciplines, including plant
morphology and protein structural analysis. In this survey article, we present
a comprehensive overview of the Euler characteristic transform, highlighting
the main idea on a simple leaf example, and surveying its its key concepts,
theoretical foundations, and available applications.
