  Topological phases of matter are often understood and predicted with the help
of crystal symmetries, although they don't rely on them to exist. In this
chapter we review how topological phases have been recently shown to emerge in
amorphous systems. We summarize the properties of topological states and
discuss how disposing of translational invariance has motivated the surge of
new tools to characterize topological states in amorphous systems, both
theoretically and experimentally. The ubiquity of amorphous systems combined
with the robustness of topology has the potential to bring new fundamental
understanding in our classification of phases of matter, and inspire new
technological developments.
