The use of sensor technology constantly gathering aircrafts' status data has promoted the rapid development of data-driven solutions in aerospace engineering. These methods assist, for instance, with determining appropriate actions for aircraft maintenance, repair and overhaul (MRO). Challenges however are found when dealing with such large amounts of data. Identifying patterns, anomalies and faults disambiguation, with acceptable levels of accuracy and reliability are examples of complex problems in this area. Experiments using deep learning techniques, however, have demonstrated its usefulness in assisting on the analysis aircraft health data. The purpose of this paper therefore is to conduct a survey on deep learning architectures and their application in aircraft MRO. Although deep learning in general is not yet largely exploited for aircraft health, from our search, we identified four main architectures employed to MRO, namely, Deep Autoencoders, Long Short-Term Memory, Convolutional Neural Networks and Deep Belief Networks. For each architecture, we review their main concepts, the types of problems to which these architectures are employed to, the type of data used and their outcomes. We also discuss how research in this area can be advanced by identifying current research gaps and outlining future research opportunities