We study ultrafast phenomena in quantum materials. One focus lies on the transport of electrons and their angular momentum triggered by femtosecond laser pulses. The associated processes often coincide with the femtosecond time scale and, thus, terahertz frequency scale. Consequently, to study such extremely fast dynamics, we develop novel tools like ultrafast ampere-meters, ohm-meters and strong terahertz voltage sources, which greatly rely on femtosecond optical pulses and ultrabroadband terahertz electromagnetic transients. To better understand our experimental results, we work out simple theoretical models. We also explore our results directly for applications in terahertz photonics, including the development of novel emitters, detectors and modulators of broadband terahertz radiation.