Ultrafast optical spectroscopy has attained prominence due to its ability to resolve dynamics in conventional metals and semiconductors at the fundamental time scales of electron and lattice motion. In recent years, ultrafast optical techniques have become more sophisticated, making it possible to directly access fundamental material parameters in a non-contact manner. In this talk, I will begin with an overview of concepts in ultrafast optical spectroscopy, including both conventional and more recently developed experimental techniques. I will then describe the use of ultrafast optical spectroscopy to study novel phenomena in a variety of complex quantum materials, including tracking carriers through space and time in individual semiconductor nanowires, unraveling the coupling between magnetic and ferroelectric order in multiferroic oxides, and directly driving lattice vibrations in a topological insulator. Overall, our studies demonstrate the utility of ultrafast optical spectroscopy in shedding light on both static and dynamic properties of complex quantum materials.