Quantum materials such as topological insulators, Weyl-semimetals, and atomically thin two-dimensional crystals have intriguing electronic properties, which makes them promising candidates for their potential applications in next-generation technology. Therefore, it is desirable to investigate the electronic properties of these materials, perhaps through various methods such that their full potential, as well as the limitations, can be identified. In this talk, I will introduce a novel spectroscopic approach based on the use of strong ultrafast laser pulses and the generation of high-order harmonics. Analysis of temporal and spectral properties of high-order harmonics from these materials reveals their valence charge density distributions, electronic band-structure, topology, as well as driven electron dynamics in the natural time scales of electrons. The advantages of this approach over conventional methods include the use of the all-optical setting, no physical contacts to samples, and much of the measurements that can be performed in ambient conditions. More importantly, the non-perturbative interaction to strong laser pulses forms novel quantum phases, which could be probed by analyzing high-order harmonics.