  Many materials crystallize in structure types that feature a square-net of
atoms. While these compounds can exhibit many different properties, some
members of this family are topological materials. Within the square-net-based
topological materials, the observed properties are rich, ranging for example
from nodal-line semimetals to a bulk half-integer quantum Hall effect. Hence,
the potential for guided design of topological properties is enormous. Here we
provide an overview of the crystallographic and electronic properties of these
phases and show how they are linked, with the goal of understanding which
square-net materials can be topological, and to predict additional examples. We
close the review by discussing the experimentally observed electronic
properties in this family.
