Deep learning has attracted intense interest in Prognostics and Health Management (PHM), because of its enormous representing power, automated feature learning capability and best-in-class performance in solving complex problems. This paper surveys recent advancements in PHM methodologies using deep learning with the aim of identifying research gaps and suggesting further improvements. After a brief introduction to several deep learning models, we review and analyze applications of fault detection, diagnosis and prognosis using deep learning. The survey validates the universal applicability of deep learning to various types of input in PHM, including vibration, imagery, time-series and structured data. It also reveals that deep learning provides a one-fits-all framework for the primary PHM subfields: fault detection uses either reconstruction error or stacks a binary classifier on top of the network to detect anomalies; fault diagnosis typically adds a soft-max layer to perform multi-class classification; prognosis adds a continuous regression layer to predict remaining useful life. The general framework suggests the possibility of transfer learning across PHM applications. The survey reveals some common properties and identifies the research gaps in each PHM subfield. It concludes by summarizing some major challenges and potential opportunities in the domain.