Summary: As timely incipient fault diagnosis is the key to guarantee operation safety and suppress fault deterioration, this paper gives a review of data driven-based researches for incipient faults, which have low amplitude and may be covered by system disturbance and noise easily. Data driven-based incipient fault diagnosis can be divided into three parts, i.e., statistical analysis-based technology, signal processing-based technology, artificial intelligence-based technology. Their basic ideas, research progresses, application and limitations are discussed in detail. Furthermore, this paper not only points out the existing problems about complex systems, but also looks forward to the advance of this area by means of adding new information, mining unused implied information, using new mathematical tools. Finally, four thoughts worth exploring are proposed: diagnosis based on correlation analysis, multi-source information fusion, machine learning and time-frequency transform.