I’ll give a pedagogical introduction to some conceptual aspects of quantum materials in and out of equilibrium. Such materials, capable of realising exotic states of matter, hold promise for manifold applications in areas like microelectronics and quantum computing. The most basic quantum materials are electronic band insulators. My talk will start with an explanation of how they can be categorised based on crystalline symmetry and topology. Following this, I will broaden the framework of band topology to include non-Hermitian Hamiltonians, which describe systems that are not in equilibrium. To conclude my talk, I will delve into a curious connection between Hermitian bulk and non-Hermitian boundary topological invariants.