There is an increasing interest in researchers and companies on the combination of Distributed Acoustic Sensing (DAS) and a Pattern Recognition System (PRS) to detect and classify potentially dangerous events that occur in areas above fiber optic cables deployed along active pipelines, aiming to construct pipeline surveillance systems. This paper presents a review of the literature in what respect to machine learning techniques applied to pipeline surveillance systems based on DAS+PRS (although its scope can also be extended to any other environment in which DAS+PRS strategies are to be used). To do so, we describe the fundamentals of the machine learning approaches when applied to DAS systems, and also do a detailed literature review of the main contributions on this topic. Additionally, this paper addresses the most common issues related to real field deployment and evaluation of DAS+PRS for pipeline threat monitoring, and intends to provide useful insights and recommendations in what respect to the design of such systems. The literature review concludes that a real field deployment of a PRS based on DAS technology is still a challenging area of research, far from being fully solved.