Experiments on quantum materials have uncovered many interesting quantum phases ranging from superconductivity to a variety of topological quantum matter including the recently observed fractional quantum anomalous Hall insulators. The findings have come in parallel with the development of approaches to probe the rich excitations inherent in such systems. In contrast to observing electrically charged excitations, the detection of charge-neutral electronic excitations in condensed matter remains difficult, although they are essential to understanding a large class of strongly correlated phases. Low-energy neutral excitations are especially important in characterizing unconventional phases featuring electron fractionalization, such as quantum spin liquids, spin ices and insulators with neutral Fermi surfaces. In this Perspective, we discuss searches for neutral fermionic, bosonic or anyonic excitations in unconventional insulators, highlighting theoretical and experimental progress in probing excitonic insulators, new quantum spin liquid candidates and emergent correlated insulators based on two-dimensional layered crystals and moiré materials. We outline the promises and challenges in probing and using quantum insulators, and discuss exciting new opportunities for future advancements offered by ideas rooted in next-generation quantum materials, devices and experimental schemes. Searches for neutral fermionic, bosonic or anyonic excitations in unconventional insulators are discussed, and challenges in probing and using quantum insulators outlined, in this Perspective on future advancements offered by quantum materials and experimental schemes.