The terahertz frequency range, 0.1-10 THz, is one of the richest frequency ranges in condensed matter spectroscopy. Many important excitations and dynamical phenomena occur in this range, including superconducting gaps, protein conformational modes, phonons, and plasmons, just to name a few. Spectroscopic studies in this region provide valuable insights into the quantum states and dynamics of confined, driven, or interacting electrons in solids. In this dissertation research I have developed a time-domain THz magneto-spectroscopy system to investigate various THz magnetic excitations in semiconductors, including a high-mobility two-dimensional electron gas (2DEG) in a GaAs quantum well and lightly-doped InSb. In the 2DEG, I have observed very long-lived (up to ∼ 50 ps) coherent THz oscillations, which correspond to a time-domain observation of cyclotron resonance. From the data both the real and imaginary parts of the conductivity can be simultaneously determined because of the phase-sensitive-detection nature of this technique. Magnetic field and temperature dependent results provide some important information on electron scattering in this system. In InSb, I have found that the THz transmittance of the sample sensitively changes with the temperature and magnetic field, showing a number of non-intuitive spectral features. In particular, I observed a sudden appearance and disappearance of transparency with increasing temperature, which resulted in a transparency window of a narrow temperature region (160-190 K), over a frequency range of 0.1-0.8 THz. Detailed theoretical simulations based on a cold magneto-plasma model demonstrate that this novel phenomenon is a manifestation of coherent interference of the cyclotron-resonance-active and cyclotron-resonance-inactive modes co-propagating through the magneto-plasma along the magnetic field direction. Finally, I have obtained some experimental results on the 1s--2p-- impurity transition at 1.6 K that provide insight on the nature of the magnetic-field-induced metal-to-insulator transition that is known to occur in this system. The materials studied in this research are highly tunable with external fields and doping and thus promising for future THz devices such as tunable THz detectors, filters, and Faraday rotators.