By adapting transmission parameters such as the constellation size, coding rate, and transmit power to instantaneous channel conditions, adaptive wireless communications can potentially achieve great performance. To realize this potential, accurate channel state information (CSI) is required at the transmitter. However, unless the mobile speed is very low, the obtained CSI quickly becomes outdated due to the rapid channel variation caused by multi-path fading. Since outdated CSI has a severely negative impact on a wide variety of adaptive transmission systems, prediction of future channel samples is of great importance. The traditional stochastic methods, modeling a time-varying channel as an autoregressive process or as a set of propagation parameters, suffer from marginal prediction accuracy or unaffordable complexity. Taking advantage of its capability on time-series prediction, applying a recurrent neural network (RNN) to conduct channel prediction gained much attention from both academia and industry recently. The aim of this article is to provide a comprehensive overview so as to shed light on the state of the art in this field. Starting from a review on two model-based approaches, the basic structure of a recurrent neural network, its training method, RNN-based predictors, and a prediction-aided system, are presented. Moreover, the complexity and performance of predictors are comparatively illustrated by numerical results.