Terahertz time-domain spectroscopy (TTDS) is a powerful spectroscopic technique, combining pulsed broadband operation with high sensitivity coherent detection at room temperature. This thesis describes studies of terahertz surface plasmon polariton (SPP) guidance on a range of metamaterial structures using TTDS. Metamaterials are artificial media constructed from sub-wavelength dimension conducting elements which have an electromagnetic response that can be engineered by creating geometrical plasma-like resonances. In this work, high-confinement terahertz waveguiding is achieved by binding SPPs to cavity resonances which spoof the behaviour of intrinsic surface plasmon resonances found at much higher frequencies. The main aim of these studies is to investigate their properties with regard to potential applications in waveguiding and sensing. The first two chapters of this thesis describe the background to the subject. In chapter 3, the construction of a novel, flexible geometry, fibre-coupled TTDS system using hollow-core photonic crystal fibre (HC-PCF) is described. The extension of the system to include a near-field probe for evanescent field characterisation is also discussed. In chapter 4, we present the first direct observation of terahertz SPP propagation on plasmonic metamaterials consisting of copper sheets patterned with two-dimensional arrays of square copper-lined holes. Wavelength-scale field confinement is experimentally observed over an octave in frequency close to the band edge, representing a two order of magnitude increase in confinement compared to a flat metal sheet. In chapter 5, metamaterials consisting of two-dimensional arrays of coaxial apertures are shown to support two spoof plasmon modes below the band edge, enabling wavelength-scale field confinement to be experimentally realised at two distinct frequencies. In chapter 6, we present the first experimental results for terahertz SPP propagation on helical and discretely grooved cylindrical metamaterials termed metawires. In each case the results are compared with numerical simulations.