  Topological materials are quantum materials with nontrivial ground-state
entanglement that are irremovable so long as certain rules, like invariance
under symmetries and the existence of an energy gap, are respected. They
showcase unconventional properties like robust anomalous surface states and
quantized physical responses. The intense research efforts in understanding
topological materials result in a modernized perspective on the decades-old
theory of symmetry representations in electronic band structures, and inspire
the development of general theories that enable the efficient diagnosis of
topological materials using only symmetry data. One example is the theory of
symmetry indicators of band topology, which is the focus of this topical
review. We will aim at providing a pedagogical introduction to the key concepts
and constructions in the theory, alongside with a brief summary of the latest
development.
