Speech emotion recognition (SER) plays an extremely important role in the process of human-computer interaction (HCI), which has attracted much attention in recent years. At present, most SER approaches are mainly trained and tested on a single emotion corpus. In practical applications, however, the training set and testing set may come from different emotion corpora. Due to the huge difference in the distribution of different emotion corpora, the cross-corpus recognition performance achieved by most SER methods is unsatisfactory. To address this issue, many researchers have started focusing on the studies of cross-corpus SER methods in recent years. This study systematically reviews the research status and progress of cross-corpus SER methods in recent years. In particular, the application of the newly developed deep learning techniques on cross-corpus SER tasks is analyzed and summarized. Firstly, the emotion corpora commonly used in SER are introduced. Then, on the basis of deep learning techniques, the research progress of existing cross-corpus SER methods based on hand-designed features and deep features is summarized and compared from the perspectives of supervised, unsupervised, and semi-supervised learning. Finally, the challenges and opportunities in the field of cross-corpus SER are discussed and predicted.