This thesis will cover my work relating to the developing eld of terahertz (THz) science and technology. It will present experimental and theoretical studies investigating the optical and electrical properties of various material systems using novel THz imaging and spectroscopy techniques. Due to its low photon energy, THz imaging and spectroscopy are useful tools for non-contact, non-destructive probing of materials. Broadband, single-cycle THz pulses are prepared using modern THz generation technology. Using the THz detection techniques of THz raster imaging and THz time-domain spectroscopy (THz-TDS), the local carrier dynamics of nanomaterials such as graphene and carbon nanotubes were determined. THz measurements on single-layer graphene grown with dierent recipes and on various substrates exhibit sub-millimeter spatial inhomogeneity of sheet conductivity. THz transmission data reveals that a thin plastic, polymethyl methacrylate (PMMA), layer in contact with single-layer graphene induces a small yet noticeable reduction in conductivity. Ulterior THz measurements performed on vertically-aligned multi-walled carbon nanotubes (V-MWCNT) employ time-resolved THz transmission ellipsometry. The angle- and polarization-resolved transmission measurements reveal anisotropic characteristics of the THz electrodynamics in V-MWCNT. The anisotropy is, however, unexpectedly weak: the ratio of the tube-axis conductivity to the transverse conductivity, ~2.3, is nearly constant over the broad spectral range of 0.4-1.6 THz. The relatively weak anisotropy and the strong transverse electrical conduction indicate that THz elds readily induce electron transport between adjacent shells within the multi-walled carbon nanotubes. In-depth coverage of the development of a high-eld THz generation system based on a lithium niobate prism will be presented. The evolution of techniques in the realm of high power THz generation is ongoing. The resolved issues throughout implementation include: magnesium doping, phase matching, and wave front distortion. The high power, broadband THz emitter (maximum THz field, Emax > 1 MV/cm) allows for nonlinear THz spectroscopy of various material systems including single-layer graphene and high-resistivity, bulk GaAs. THz-induced transparency is observed in two types of single-layer graphene samples: (i) suspended graphene-PMMA layer and (ii) graphene embedded in dielectrics. THz-induced transparency is shown to be signicantly higher in suspended graphene than in graphene on a Si substrate. The experimental observation leads to a universal nonlinear THz property of graphene that the sheet conductivity undergoes twofold reduction when THz elds reach 0:8 MV/cm. We conrm the generality of this result by measuring dierent graphene samples on dierent substrates. Timeresolved THz transmission measurements show that the THz-induced transparency in graphene is dynamic; the transient conductivity gradually decreases throughout the pulse duration. The large THz elds induce sub-picosecond electron thermalization and subsequent carrier-carrier scattering, transiently modulating the electrical and optical properties, in eect reducing the electrical conductivity of graphene by an order of magnitude. Nonlinear THz spectroscopy methods are also applied to the investigation of a nano-antenna patterned, high-resistivity, intrinsic GaAs wafer. The antenna near-eld reaches 20 MV/cm due to a huge eld enhancement in the plasmonic nanostructure. Thus, the nonlinear THz interactions take place in the conned nanometer-scale region adjacent to the antenna. As a result of the huge THz elds, nano-antenna patterned GaAs demonstrates remarkably strong nonlinear THz eects. The elds are strong enough to generate high density free carriers (Ne > 10^17 cm^3) via high-energy interband excitations associated with a series of impact ionizations (n_I ~ 33-37); thus inducing large absorption of THz radiation (> 35%).