Data-based process monitoring has become a key technology in process industries for safety, quality, and operation efficiency enhancement. This paper provides a timely update review on this topic. First, the natures of different industrial processes are revealed with their data characteristics analyzed. Second, detailed terminologies of the data-based process monitoring method are illustrated. Third, based on each of the main data characteristics that exhibits in the process, a corresponding problem is defined and illustrated, with review conducted with detailed discussions on connection and comparison of different monitoring methods. Finally, the relevant research perspectives and several promising issues are highlighted for future work.