Probabilistic linguistic term set (PLTS), which consists of multiple linguistic terms and their probabilities, has been proposed to tackle qualitative information in informs of linguistic expressions. Since experts are inclined to compare alternatives in pairs, the probabilistic linguistic preference relation (PLPR), a matrix whose elements are PLTSs, has attracted wide attention since it was first introduced in 2016. Fruitful research achievements regarding PLPRs have been generated, especially in group decision making (GDM). This paper reviews 88 selected articles published from 2016 to June 4, 2023 regarding PLPRs, and presents a review of researches on theory and applications of PLPRs. First, we conduct a bibliometric study of these selected articles in terms of publication and citation trends, most productive countries/regions, categories of publications and keyword co-occurrence relationships. Next, the theory of PLPRs including definition, missing element deduction, consistency checking, prioritization, and decision-making analysis methods are recalled. We also review real-world applications of these publications and find that PLPRs have been mainly applied in four areas, including healthcare management, project evaluation, environment and energy management, and emergency management. In the end, we propose future research directions related to the probabilistic linguistic decision-making theory and provide insights for researchers and practitioners who have an interest in complex linguistic decision making.