Transformers, which transfer electrical power between voltage levels, are very important electrical power system components whose unforeseen breakdowns may lead to huge losses in finances and extensive power cuts. Thus, fault detection and diagnosis require good performance to provide reliability, operational safety, and service life of the transformers. Multi-Agent Systems (MAS) have become a potential paradigm of intelligent fault detection in transformers over the last twenty years, with respect to distributed and autonomous fault detection. A structured literature review is provided in this paper on the existing body of literature that explores the use of MAS in transformer fault detection and its application in other fields of power systems in general. The studies reviewed are grouped by the authors into five thematic classes: MAS architectures to monitor transformer condition, MAS to complement Dissolved Gas Analysis (DGA), MAS to identify damaged power distribution system faults, MAS as a hybrid AI approach, and basic MAS structures with safety in mind. Close attention is given to collaborative and distributed diagnostic methods, such as Bayesian networks, Multiply Sectioned Bayesian Networks, Dempster-Shafer evidence theory, fuzzy ontology- based reasoning, and new methods, such as digital twins and knowledge graph-based fault localization. The review makes clear that MAS architectures are very beneficial in terms of modularity, scalability, and real-time diagnostic capability, and that the combination of artificial intelligence and machine learning techniques can lead to a significant improvement in the accuracy of the fault classification. Moreover, the paper pinpoints the research gaps that are critical, especially those that exist in the fields of uniform inter-agent communication protocols, ontology-based reasoning, reproducibility and benchmarking, real-world large-scale implementation, and quantum-enhanced MAS. Lastly, it provides future research directions for the future development of MAS-based transformer fault detection and diagnosis.