Quantum materials are defined by the emergence of new properties resulting from collective quantum effects and by holding promise for their quantum applications. Novel superconductors, from high-Tc cuprates and iron-based superconductors to twisted monolayers, exhibit a higher level of emergent complexity, with a multiband electronic structure playing a pivotal role in their comprehension and potential applications. Here, we provide a brief overview of key multiband effects in these superconductors and topological semimetals, offering guidelines for the theory-assisted development of new quantum materials and devices.