Quantum-confined semiconductor structures are ideal systems in which to study non-equilibrium and coherent dynamics of interacting many particles in a highly controllable fashion. In particular, two-dimensional (2D) semiconductor systems in a strong perpendicular magnetic field provide one of the cleanest condensed matter systems with ultralong coherence times, allowing us to excite and control macroscopic coherent phenomena. When doped, either electrically or optically, such systems can accommodate quantum-degenerate fermions (electrons) and/or bosons (excitons). In this dissertation, we studied the coherent terahertz (THz) dynamics of 2D gases of electrons and excitons in GaAs quantum wells in magnetic fields with time-domain THz magneto-spectroscopy. In high-mobility 2D electron gases, we made the first observation of collective radiative decay, or superradiance, of cyclotron resonance (CR). The decay rate of coherent CR oscillations increased linearly with the electron density in a wide range, which is a hallmark of superradiant damping. Our fully quantum mechanical theory provided a universal formula for the decay rate. We further achieved ultrastrong coupling of coherent CR with THz photons in a high quality factor 1D photonic crystal cavity. We directly observed time-domain vacuum Rabi oscillations, and the square root of N dependence of collective Rabi splitting with respect to the carrier density. Superradiance decay of CR was significantly suppressed in the cavity, and an intrinsic CR linewidth as sharp as 5.6~GHz was resolved. In undoped GaAs quantum wells, we systematically investigated the nonequilibrium dynamics of electron-hole pairs using ultrafast optical-pump THz-probe spectroscopy. We simultaneously monitored the intraexcitonic 1s-2p transition, which splits into the 1s-2p+ and 1s-2p- transitions in a magnetic field, and the CR of unbound carriers as a function of pair density, temperature, magnetic field, and probe delay time. We found that the 1s-2p- feature is robust at high magnetic fields even under high excitation fluences, indicating magnetically enhanced stability of excitons. While mimicking some of the well-known phenomena in quantum optics of atomic and molecular gases, these results highlight some of the unique features of condensed matter systems due to strong many-body Coulomb interactions among carriers and open a door to the novel physics of THz many-body electrodynamics.