Myocardial infarction is a common cardiovascular disorder caused by prolonged ischemia, and early diagnosis of myocardial infarction (MI) is critical for lifesaving. ECG is a simple and non-invasive approach in MI detection, localization, diagnosis, and prognosis. Population-based screening with ECG can detect MI early and help prevent it but this method is too labor-intensive and time-consuming to carry out in practice unless artificial intelligence (AI) would be able to reduce the workload. Recent advances in using deep learning (DL) for ECG screening might rekindle this hope. This review aims to take stock of 59 major DL studies applied to the ECG for MI detection and localization published in recent 5 years, covering convolutional neural network (CNN), long short-term memory (LSTM), convolutional recurrent neural network (CRNN), gated recurrent unit (GRU), residual neural network (ResNet), and autoencoder (AE). In this period, CNN obtained the best popularity in both MI detection and localization, and the highest performance has been obtained from CNN and ResNet model. The reported maximum accuracies of the six different methods are all beyond 97%. Considering the usage of different datasets and ECG leads, the network that trained on 12 leads ECG data of PTB database has obtained higher accuracy than that on smaller number leads data of other datasets. In addition, some limitations and challenges of the DL techniques are also discussed in this review.