Pipeline networks have been widely utilised in the transportation of water, natural gases, oil and waste materials efficiently and safely over varying distances with minimal human intervention. In order to optimise the spatial use of the pipeline infrastructure, pipelines are either buried underground, or located in submarine environments. Due to the continuous expansion of pipeline networks in locations that are inaccessible to maintenance personnel, research efforts have been ongoing to introduce and develop reliable detection methods for pipeline failures, such as blockages, leakages, cracks, corrosion and weld defects. In this paper, a taxonomy of existing pipeline failure detection techniques and technologies was created to comparatively analyse their respective advantages, drawbacks and limitations. This effort has effectively illuminated various unaddressed research challenges that are still present among a wide array of the state-of-the-art detection methods that have been employed in various pipeline domains. These challenges include the extension of the lifetime of a pipeline network for the reduction of maintenance costs, and the prevention of disruptive pipeline failures for the minimisation of downtime. Our taxonomy of various pipeline failure detection methods is also presented in the form of a look-up table to illustrate the suitability, key aspects and data or signal processing techniques of each individual method. We have also quantitatively evaluated the industrial relevance and practicality of each of the methods in the taxonomy in terms of their respective deployability, generality and computational cost. The outcome of the evaluation made in the taxonomy will contribute to our future works involving the utilisation of sensor fusion and data-centric frameworks to develop efficient, accurate and reliable failure detection solutions.