The Global Positioning System (GPS) has motivated rapid advances in mobility data collection. A massive amount of spatio-temporal information has made it possible to know where a person was and when, but not how and why (s)he travelled, creating the need for inference models. Compared with mode detection, purpose imputation has been insufficiently studied. However, the relative lack of attention to purpose identification does not mean that this field has not emerged. For this paper, which is the first review dedicated to inferring trip purposes from GPS data, 1,162 non-duplicate papers from four databases (Scopus, Web of Science, ScienceDirect and TRID) were screened, and a corpus of 25 publications was selected for examination. Based on these papers, the purpose imputation problem is defined in the contexts of the evolution of GPS-based travel surveys and two research domains, Transportation Science (TS) and Human Geography (HG). Subsequently, three steps of the purpose detection process, namely (1) trip end detection, (2) input feature selection and (3) main algorithms and validation, are surveyed. During these procedures, the differences between studies in TS and those in HG are highlighted. Finally, unresolved issues related to data and feature selection, algorithms and assessment are discussed substantially to provide potential research directions. This review may be an informative reference for those newly accessing the GPS-based purpose imputation field and/or intending to develop solutions to this problem.