Interval time series forecasting can be used for forecasting special symbolic data comprising lower and upper bounds and plays an important role in handling the complexity, instability, and uncertainty of observed objects. The purpose of this research is to identify the most widely used definition of interval time series; classify existing research into mature research, current research focus, and research gaps within the defined framework; and recommend future directions for interval forecasting research. To achieve this goal, we have conducted a systematic literature review, comprising search strategy planning, screening mechanism determination, document analysis, and report generation. During the search strategy planning stage, eight literature search libraries are selected to obtain the most extensive studies (total of 525 targets). In the screening‐mechanism determination stage, through the inclusion and exclusion mechanism, the literature that is repetitive, of low‐relevance, and from other fields are discarded, and 125 studies are finally selected. In the document analysis stage, tag‐based methods and classification grids are selected to analyze the shortlisted studies. The results show that there are still numerous research gaps in interval time series forecasting, such as the establishment of hybrid models, application of multisource information, development and application of evaluation techniques, and expansion of application scenarios. In the report‐generation stage, the problems that have been solved and encountered in interval forecasting are summarized, and future research directions are proposed. Finally, the most significant contribution of this research is to provide an overview of interval time series forecasting for easy reference by researchers and to facilitate further research.