Time-resolved terahertz (THz) spectroscopy is an emerging optical characterization technique with the potential of becoming standard practice in fundamental research and in industry. These systems have the ability to be extremely broadband and can retrieve the phase and amplitude information of a THz pulse transmitted through a material, allowing the complex dielectric function of the material to be extracted. Although these systems are already extremely impactful, they nonetheless have their shortcomings. Namely, the data acquisition time required for a single measurement hinders their practicality in an industrial setting or retrieving interesting dynamics within a sample that are occurring on faster timescales. Moreover, broadband THz systems carry a significant financial burden as they rely on ultrafast near-infrared (NIR) sources delivering sub-100 fs pulses, limiting their accessibility. In this work, we address these issues plaguing time-resolved THz systems with the implementation of optical fibers. We begin by describing the physical processes governing ultrashort pulse propagation in fiber and the generation and detection of THz pulses via nonlinear effects in semiconductor crystals. We then design and demonstrate a THz detection scheme able to resolve each of the generated THz pulses at a repetition rate of 50 kHz. This includes using fiber to generate a chirped NIR supercontinuum, imprinting THz waveforms onto the NIR spectrum and thereby enabling single-shot THz detection; and using fiber to achieve photonic time-stretch, a technique allowing us to detect each of the THz-encoded NIR pulses with high-speed electronics at a rate determined by the repetition rate of the laser. The resulting system is then used to track carrier dynamics in a semiconductor as they are dynamically accumulating and recombining. We then combine nonlinear propagation in optical fiber with a time-resolved THz system allowing us to achieve broadband THz generation and detection. We describe two systems relying on this general scheme: The first system relies on a compact and cost-effective laser source and a standard fiber to generate and detect a THz spectrum extending up to 6 THz, alleviating the financial strain imposed by systems relying on sophisticated laser sources without sacrificing performance. The other system relies on an amplified laser source and gas-filled hollow-core photonic crystal fiber (PCF) to generate a tunable spectrum up to 20 THz. Finally, we investigate the generation of a supercontinuum spanning more than two octaves inside a highly nonlinear solid-core PCF. For the first time, we explore both the spectral intensity and polarization structure of such a broad optical spectrum approaching the mid-infrared region.