A multi-omics dataset combining clinical features with the discovery of biomarkers could contribute significantly to the timely identification of mortality risk and the develop- ment of personalized therapies for a wide range of diseases, including cancer and stroke. As well, new advances in “omics” technologies can open up a lot of possibilities for researchers to find disease biomarkers through system-level analysis. Machine learning methods, es- pecially based on tensor decomposition methods (TD-based), are becoming more popular because the integrative analysis of multi-omics data is challenging due to biological com- plexity. Therefore, it is important to identify future research directions and opportunities on the topic of biomarker discovery using tensor decompositions in multi-omics datasets by integrating literature reviews. This article systematically reviews the research trends from 2015 to 2022. Several themes are discussed, including challenges and problems of de- veloping and applying tensor decompactions, application areas for biomarker discovery in “omics” datasets, proposed methodologies, key evaluation criteria used in deciding whether the new methods are effective, and the limitations and shortcomings of this field, which call for further research and development. This review helps researchers who are interested in this field understand what research has already been done and where potential areas for future research might lie.