Understanding and manipulating quantum superposition are important quests in quantum materials research. One exciting direction emerging in the field is to use the geometry of quantum states – the so-called quantum geometry – as a means of characterizing quantum superposition. This approach has successfully characterized various electric and magnetic properties of materials, which are not easily captured by semiclassical approaches. In this seminar, I will first introduce a general theory of the quantum geometry of resonant optical electric-dipole responses in materials. I will discuss the new insights from this quantum-geometric paradigm, guiding us to discover and investigate new optical phenomena. In the second part, I will talk about an intriguing optical response going beyond electric-dipole transitions: a surprising Kerr effect in certain antiferromagnets that are non-quantized but owe their existence to axion electrodynamics. This response has recently been observed in experiments and used for the optical control of antiferromagnets. Finally, I will give an outlook for future directions.