Supply chain management (SCM) encompasses a wide variety of decision-making problems that affect business and supply chain performance. Since most of these problems involve uncertainty and hesitation on the part of decision makers (DMs), various studies have emerged recently that present SCM applications of techniques based on Hesitant Fuzzy Linguistic Term Sets (HFLTSs) and HFLTS extensions. Given the relevance of this subject and the lack of literature review studies, this study presents a systematic review of HFLTS and HFLTS extension applications to SCM decision-making problems. In order to answer a set of research questions, the selected papers were classified in accordance with a group of factors that are pertinent to the origins of these studies, SCM, HFLTSs, and decision making. The results demonstrated that the Source and Enable processes have been studied with greater frequency, while the most common problems have to do with supplier selection, failure evaluation, and performance evaluation. The companies of the automotive sector predominated in the analyzed studies. Even though most of the studies used techniques based on HFLTSs, we identified applications of seven distinct HFLTS extensions. The main contribution of this study consists of presenting an overview of the use of HFLTSs and their extensions in practical examples of SCM, highlighting trends and research opportunities. It is the first study to analyze applications of decision-making techniques that deal with hesitation in SCM. Therefore, the results can help researchers and practitioners develop new studies that involve the use of HFLTSs and HFLTS extensions in decision-making problems, given that this study systematizes elements that should be considered in the modeling, application, and validation of these methods.