The accurate forecast of air temperature plays an important role in water resources management, land–atmosphere interaction, and agriculture. However, it is difficult to accurately predict air temperature due to its non-linear and chaotic nature. Several deep learning techniques have been proposed over the last few decades to forecast air temperature. This study provides a comprehensive review of artificial neural network (ANN)-based approaches (such as recurrent neural network (RNN), long short-term memory (LSTM), etc.), which were used to forecast air temperature. The focus is on the works during 2005–2020. The review shows that the neural network models can be employed as promising tools to forecast air temperature. Although the ANN-based approaches have been utilized widely to predict air temperature due to their fast computing speed and ability to deal with complex problems, no consensus yet exists on the best existing method. Additionally, it is found that the ANN methods are mainly viable for short-term air temperature forecasting. Finally, some future directions and recommendations are presented.