The aim of this thesis is to develop procedures for the modelling and inversion of teleseismic P and S waveforms which are as flexible as possible. This flexibility is necessary in order to obtain accurate source depth and mechanism estimates for small to moderate size events, such as those that are relevant in the context of monitoring the Comprehensive Nuclear-Test-Ban Treaty (CTBT). ¶ The main challenge for extending source depth and mechanism inversion methods to smaller events is to ensure that sufficiently accurate synthetic seismograms are available for comparison with observed records. An accurate phase-adaptive reflectivity method has therefore been developed, against which the performance of less computationally intensive approximations can be judged. The standard reflectivity method has been modified to allow for different crustal and upper mantle structures at the source and receiver, and the full effects of reverberations and conversions in these structures can be allowed for. Core reflections and refractions can also be included; these phases can become important at certain distance ranges. A slowness bundle approach has been developed, where a restricted slowness integration about the geometric slowness for the direct wave is undertaken at each frequency, allowing accurate results to be obtained whilst avoiding the expense of a full reflectivity technique. ¶ Inversion using the neighbourhood algorithm (NA) is performed for source depth, mechanism and time function, by modelling direct P and S and their surface reflections (pP, sP and pS, sS) at teleseismic distances. Both SV and SH data are exploited in the inversion, in addition to P data, in order to obtain improved constraints on the source mechanism, including any isotropic component. Good results are obtained using a simple generalised ray scheme, however, the use of a flexible derivative-free inversion method means that more accurate synthetics are able to be used in the inversion where appropriate. The NA makes use of only the rank of the data misfits, so that it is possible to employ any suitable misfit criterion. In the few cases where control on the source mechanism is limited, good depth resolution is still usually obtained. ¶The structures near the source and receiver play an important role in shaping the detail of the teleseismic waveforms. Although reasonable results can be achieved with simple synthetics and a standard velocity model, significant improvement can be made by modifying the representation of structure near the source and receiver. In the case of sub-oceanic events it is important to allow for the effects of water reverberations. The crustal structure near the receiver can also have quite a large influence on the waveforms through reverberations and conversions. This is exploited in receiver function inversion, which is again accomplished using the NA approach.