Spectrally efficient methods of digital transmission are studied, with particular emphasis on vestigial sideband (VSB) signalling. A general overview of digital transmission techniques gives a basis for more detailed studies into the areas of interest. Alternative methods of generating and detecting VSB are covered, offering possible ways of simplifying system implementation. A method of synchronizing VSB is proposed and analysed, giving a simple solution to the synchronization problem. VSB, as a spectrally efficient signalling format, is shown to be suitable for transmission over nonlinear channels; its performance comparing favourably with alternative systems. A new method of attaining spectrally efficient transmission is analysed. This combines VSB and quadrature modulation to obtain a signal with double the spectral efficiency of VSB. With suitable decoding this increased spectral efficiency is obtained at the expense of only a small sacrifice in power efficiency.