Artificial intelligence has undergone rapid development in the last thirty years and has been widely used in the fields of materials, new energy, medicine, and engineering. Similarly, a growing area of research is the use of deep learning (DL) methods in connection with hydrological time series to better comprehend and expose the changing rules in these time series. Consequently, we provide a review of the latest advancements in employing DL techniques for hydrological forecasting. First, we examine the application of convolutional neural networks (CNNs) and recurrent neural networks (RNNs) in hydrological forecasting, along with a comparison between them. Second, a comparison is made between the basic and enhanced long short-term memory (LSTM) methods for hydrological forecasting, analyzing their improvements, prediction accuracies, and computational costs. Third, the performance of GRUs, along with other models including generative adversarial networks (GANs), residual networks (ResNets), and graph neural networks (GNNs), is estimated for hydrological forecasting. Finally, this paper discusses the benefits and challenges associated with hydrological forecasting using DL techniques, including CNN, RNN, LSTM, GAN, ResNet, and GNN models. Additionally, it outlines the key issues that need to be addressed in the future.