This thesis investigates Graphene, a gapless semi-conductor with relativistic-like electron behaviour, using on-chip terahertz time-domain spectroscopy (OC-THz-TDS). In this technique single-cycle THz frequency pulses are emitted, guided by waveguides, and detected on a single chip. The device fabrication is achieved by incorporating planar Goubau line waveguides with epitaxial GaAs and graphene grown by chemical vapour deposition. Spectroscopy of these devices, with graphene spanning a small gap between the waveguides, reveals large oscillations that are mainly attributed to the gap and other waveguide features. Optical-pump terahertz-probe measurements are used to isolate the contribution of the graphene sample, and to observe the (picosecond timescale) hot-carrier lifetime. The ultrafast carrier dynamics of graphene are then applied to demonstrate the first known measurements of graphene as an on-chip terahertz photoconductive detector; operating at frequencies up to 600 GHz. Pulsed terahertz emission from graphene is also demonstrated for a range of bias voltages, and considerations towards the design of all-graphene on-chip terahertz devices is discussed. The spatial dependence of picosecond pulse detection using graphene is also investigated, achieved by mapping the optical probe location for a variety of switch geometries. A better understanding of the interaction of the terahertz field with the graphene over distances of 50 to 200 um is obtained, which may be used to improve performance and build towards making graphene a viable option in commercial THz-TDS systems.