Depression has become one of the most common mental illnesses in the world. For better prediction and diagnosis, methods of automatic depression recognition based on speech signal are constantly proposed and updated, with a transition from the early traditional methods based on hand-crafted features to the application of architectures of deep learning. This paper systematically and precisely outlines the most prominent and up-to-date research of automatic depression recognition by intelligent speech signal processing so far. Furthermore, methods for acoustic feature extraction, algorithms for classification and regression, as well as end to end deep models are investigated and analysed. Finally, general trends are summarised and key unresolved issues are identified to be considered in future studies of automatic speech depression recognition.