The human attention mechanism can be understood and simulated by closely associating the saliency prediction task to neuroscience and psychology. Furthermore, saliency prediction is widely used in computer vision and interdisciplinary subjects. In recent years, with the rapid development of deep learning, deep models have made amazing achievements in saliency prediction. Deep learning models can automatically learn features, thus solving many drawbacks of the classic models, such as handcrafted features and task settings, among others. Nevertheless, the deep models still have some limitations, for example in tasks involving multi-modality and semantic understanding. This study focuses on summarizing the relevant achievements in the field of saliency prediction, including the early neurological and psychological mechanisms and the guiding role of classic models, followed by the development process and data comparison of classic and deep saliency prediction models. This study also discusses the relationship between the model and human vision, as well as the factors that cause the semantic gaps, the influences of attention in cognitive research, the limitations of the saliency model, and the emerging applications, to provide new saliency predictions for follow-up work and the necessary help and advice.