This survey covers the literature on the fault diagnosis and prediction of the remaining useful life of aircraft engines based on deep learning. A formal statement of the remaining useful life esti-mation problem is given. The basic architectures of deep neural networks are considered to detect rare failures and predict the next failures using aircraft engine condition monitoring data. The extraction of informative features using autoencoders is discussed. The structure of long short-term memory (LSTM) and attention mechanism (AM) cells applied in deep neural networks to predict the remaining useful life is described. The problem of integrating remaining useful life prediction into maintenance planning based on reinforcement learning is considered.