Quality assessment in industrial applications is often carried out through visual inspection, usually performed or supported by human domain experts. However, the manual visual inspection of processes and products is error-prone and expensive. It is therefore not surprising that the automation of visual inspection in manufacturing and maintenance is heavily researched and discussed. The use of artificial intelligence as an approach to visual inspection in industrial applications has been considered for decades. Recent successes, driven by advances in deep learning, present a possible paradigm shift and have the potential to facilitate automated visual inspection, even under complex environmental conditions. For this reason, we explore the question of to what extent deep learning is already being used in the field of automated visual inspection and which potential improvements to the state of the art could be realized utilizing concepts from academic research. By conducting an extensive review of the openly accessible literature, we provide an overview of proposed and in-use deep-learning models presented in recent years. Our survey consists of 196 open-access publications, of which 31.7% are manufacturing use cases and 68.3% are maintenance use cases. Furthermore, the survey also shows that the majority of the models currently in use are based on convolutional neural networks, the current de facto standard for image classification, object recognition, or object segmentation tasks. Nevertheless, we see the emergence of vision transformer models that seem to outperform convolutional neural networks but require more resources, which also opens up new research opportunities for the future. Another finding is that in 97% of the publications, the authors use supervised learning techniques to train their models. However, with the median dataset size consisting of 2500 samples, deep-learning models cannot be trained from scratch, so it would be beneficial to use other training paradigms, such as self-supervised learning. In addition, we identified a gap of approximately three years between approaches from deep-learning-based computer vision being published and their introduction in industrial visual inspection applications. Based on our findings, we additionally discuss potential future developments in the area of automated visual inspection.