This paper presents a review of deep learning on engineering drawings and diagrams. These are typically complex diagrams, that contain a large number of different shapes, such as text annotations, symbols, and connectivity information (largely lines). Digitising these diagrams essentially means the automatic recognition of all these shapes. Initial digitisation methods were based on traditional approaches, which proved to be challenging as these methods rely heavily on hand-crafted features and heuristics. In the past five years, however, there has been a significant increase in the number of deep learning-based methods proposed for engineering diagram digitalisation. We present a comprehensive and critical evaluation of existing literature that has used deep learning-based methods to automatically process and analyse engineering drawings. Key aspects of the digitisation process such as symbol recognition, text extraction, and connectivity information detection, are presented and thoroughly discussed. The review is presented in the context of a wide range of applications across different industry sectors, such as Oil and Gas, Architectural, Mechanical sectors, amongst others. The paper also outlines several key challenges, namely the lack of datasets, data annotation, evaluation and class imbalance. Finally, the latest development in digitalising engineering drawings are summarised, conclusions are drawn, and future interesting research directions to accelerate research and development in this area are outlined.