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This paper provides an overview of the applications of Convolutional Neural Networks (CNN) in the railway maintenance industry. Our research covers specifically the subdomain of railway track maintenance. In this study, we have analyzed the state-of-the-art of CNNs applied to railway track maintenance by conducting an extensive literature review, summarizing different tasks and problems related to the topic and presenting solutions based on CNNs with a special emphasis on the data used to create these models. The results of our research show different applications of CNNs within the scope, including the detection of defects in the surface of railway rails and railway track components, such as fasteners, joints, sleepers, switches and crossings, as well as the recognition of track components, and the continuous monitoring of railway tracks. The architecture of CNNs is fitting to learning spatial hierarchies of features directly from the input data, making them of great use for Computer Vision and other applications related to the topic at hand. The implementation of IoT devices and smart sensors aid the collection of real-time data which can be used to feed powerful CNN models to recognize patterns and identify complex events related to the maintenance of railway tracks. This and more insights are discussed in detail within the contents of this paper.