Atrial fibrillation (AF) is a common arrhythmia that can lead to stroke, heart failure, and premature death. Manual screening of AF on electrocardiography (ECG) is time-consuming and prone to errors. To overcome these limitations, computer-aided diagnosis systems are developed using artificial intelligence techniques for automated detection of AF. Various machine learning and deep learning (DL) techniques have been developed for the automated detection of AF. In this review, we focused on the automated AF detection models developed using DL techniques. Twenty-four relevant articles published in international journals were reviewed. DL models based on deep neural network, convolutional neural network (CNN), recurrent neural network, long short-term memory, and hybrid structures were discussed. Our analysis showed that the majority of the studies used CNN models, which yielded the highest detection performance using ECG and heart rate variability signals. Details of the ECG databases used in the studies, performance metrics of the various models deployed, associated advantages and limitations, as well as proposed future work were summarized and discussed. This review paper serves as a useful resource for the researchers interested in developing innovative computer-assisted ECG-based DL approaches for AF detection.