When light is absorbed in a material, the resulting excitations tell us a lot about the nature of that material. In semiconductor nanomaterials, the dynamics of photoexcited carriers typically evolves over ultrafast time scales from nanoseconds (billionth of a second) down to picoseconds (trillionth of a second). Time-resolved terahertz pulse spectroscopy is a powerful tool for probing ultrafast carrier dynamics in nanomaterials. This talk will provide an introduction to terahertz (THz) pulse spectroscopy, discuss how it can be applied to reveal ultrafast dynamics over nanometer length scales in materials, and present a new technique that couples THz pulses to the tip of a scanning tunneling microscope (THz-STM) and can directly image sub-picosecond carrier capture into a single semiconductor nanodot.