  Topological phases of matter have sparked an immense amount of activity in
recent decades. Topological materials are classified by topological invariants
that act as a non-local order parameter for any symmetry and condition. As a
result, they exhibit quantized bulk and boundary observable phenomena,
motivating various applications that are robust to perturbations. In this
review, we explore such a topological classification for quasiperiodic systems,
and detail recent experimental activity in the field.
