With the development of modern industry and ever more complex structural loads, the possibility of fatigue failure is increasing. Fatigue analysis can be used to evaluate the service life of components and reduce the probability of accidents. Therefore, the development and application of fatigue-analysis technology have important research significance. This paper collects information from a wide field of literature and summarizes the current status of fatigue-analysis research. It covers related theoretical knowledge, fatigue-life prediction methods, and fatigue design methods and their application scenarios, and it summarizes the challenges and research hotspots in the field. On the basis of this examination, future development directions of fatigue-life prediction methods are proposed. The conclusions will have a certain guiding role in the development of fatigue-analysis methods.