Terahertz (THz) technology stands to solve a number of problems in everyday life, from next generation wireless communication to spectroscopic identification and imaging. However it is technically challenging to make a high power, compact source for terahertz radiation. The Quantum Cascade Laser (QCL), which produces gain at THz frequencies by exploiting inter-sub-band transitions in quantum wells, offers one solution to this problem. However controlling and detecting the emission from such sources remains a major challenge. This thesis investigates the theory and measurement of emission frequencies from aperiodic lattice THz QCLs. Crucially, realising both frequency control and detection provides a complete system for coherent THz characterisation of devices at precise, user defined frequencies.The author starts by studying the emission frequencies and threshold of discretely tuned aperiodic lattice lasers. This is achieved using a numerical transfer matrix method (TMM), which allows the calculation of the aperiodic lattice threshold spectrum for the first time. Calculations reveal that the low threshold modes of aperiodic lattice lasers form at peaks in the electromagnetic density of modes. This shows that lasing in aperiodic lattices arises from slow light propagation induced by multiple photonic band gaps, leading to both band edge and defect laser modes. Frequency selective lasing is maintained even under the influence of external facet feedback, albeit at the cost of precise knowledge of the mode frequency. Importantly this framework allows the understanding of essentially any aperiodic lattice laser system. Most significantly, the TMM is exploited in order to understand how graphene can be used to control a THz laser. Graphene interacts strongly with THz waves, and can be easily integrated with semiconductor structures such as lasers and waveguides. Here, numerical calculations reveal that graphene can be introduced into the waveguide of a THz QCL, generating electrically tunable THz surface plasmons. Such surface plasmons couple into an aperiodic lattice to change the scattering strength of each individual grating element. The TMM reveals that this change in scattering strength controls the modal selectivity of an aperiodic lattice THz QCL. This hypothesis successfully explains both earlier experiments and those performed by the author. Crucially, this model was central to a publication in the journal Science.Finally, this thesis demonstrates a novel coherent detection system for the characterisation of THz QCL emission. The technique exploits non-linear up-conversion of THz waves to a telecoms frequency side-band, a process shown to be sensitive to THz waveguide dispersion. By mixing the up-converted THz wave with a near infra-red local oscillator laser, coherent detection of QCL emission using all fibre coupled components is demonstrated for the first time. This measurement allows for the characterisation of laser emission with high frequency and temporal resolution. Specifically sub-microsecond pulses of THz emission and transients can be detected. When taken as a whole, the work of this thesis constitutes a major step towards realising cost effective THz characterisation and spectroscopy using QCLs.