After more than 50 years of searching the skies across the electromagnetic spectrum, no evidence has yet been found for the existence of extraterrestrial life, let alone a signature that could be attributed to an intelligent and technological extraterrestrial civilisation. Proposed explanations range from the non-existence of such putative civilisations, to the likelihood that the search has barely "scratched the surface" in terms of covering the entire discovery space. The present work is premised on the latter position, and its central thesis is that most searches conducted thus far have been disadvantaged by sub-optimal design. In general, they have (1) not targeted the most appropriate signal types; (2) not targeted the region of the electromagnetic spectrum that should be preferred for interstellar communications; and (3) not consistently concentrated on the regions of the sky that hold the highest likelihood for the emergence of extraterrestrial intelligence. The very nature of past searches provides a credible explanation for the null result to date. It is impossible to predict the specific technologies and communications methodologies likely to be adopted by extraterrestrial civilisations, particularly when one considers how much older and more technologically advanced than ourselves they may be. However, beginning with a single key assumption – that energy efficiency is a concern to those wishing to transmit signals across interstellar space – this work shows how the application of fundamental principles of astrophysics and information theory can lead to meaningful constraints on the discovery space for artificial interstellar signals. It is shown why the search for extraterrestrial intelligence should focus on intentionally transmitted wideband signals occupying the upper end of the microwave range of the radio spectrum - a region largely ignored by past searches. Furthermore, searches should concentrate on the inner Galaxy rather than our own solar neighbourhood. A new signal processing algorithm is introduced for the blind detection of wideband signals of a class that is attractive for interstellar communications, offering high detection sensitivity while making minimal assumptions about the precise signal format. The findings of this thesis suggest a range of new priorities and approaches to the search for extraterrestrial intelligence, aimed at increasing its chances of success.