A system’s ability to create new electric fields from intense, applied electric fields offers unique insight into the quantum mechanical structure and photoexcited dynamics of the system. This dissertation describes the development, application, and modeling of new multidimensional spectroscopies along with more mature ones to investigate transition metal dichalcogenide and lead halide perovskite semiconductors which show great promise for next-generation photovoltaics and optoelectronics. First, we show that multidimensional triple sum-frequency (TSF) spectroscopy is susceptible to group and phase velocity mismatch artifacts when accomplished in a transmissive geometry with thick substrates. Using TSF in a reflective geometry, we interrogate the electronic structure of a MoS2 thin film and experimentally confirm predictions of band nesting contributions to MoS2’s optical joint density of states. We then show that TSF, when preceded by a pump, can probe the ultrafast dynamics of MoS2 and WS2 microstructures without suffering from sensitivity losses due to low surface coverage like the more common transient-reflectance spectroscopy. This work is then extended to the regime of an intense, non-resonant pump, and we demonstrate the existence of the optical Stark effect in optical harmonic generation. Next, we investigate questions relevant to material scientists. Transient-reflectance spectroscopy is employed to monitor ultrafast charge dynamics in WS2-MoS2 core-shell lateral heterostructures. After applying a Fresnel model to account for effects of the stratified substrate, we find no evidence for ultrafast charge transfer. We then use transient-transmittance and -reflectance spectroscopies to probe the hot carrier cooling and surface recombination dynamics of lead halide perovskites. Finally, we develop multidimensional harmonic generation as a probe of crystal symmetry, which is not susceptible to multiphoton photoluminescence artifacts.