Three-dimensional data are increasingly prevalent across biomedical and social domains. Notable examples are gene-sample-time, individual-feature-time, or node-node-time data, generally called observation attribute-context data. The unsupervised analysis of three-dimensional data can be pursued to discover putative biological modules, disease progression profiles, and communities of individuals with coherent behaviour, among other patterns of interest. It is thus key to enhancing the understanding of complex biological, individual, and societal systems. The clustering technique is one of the important unsupervised approaches for mining similar patterns either row-wise or column-wise. Biclustering performs simultaneous clustering of both rows and columns by identifying the similarities under a specific subset of conditions. On the other hand, the Triclustering algorithm extracts similar pattern subsets including row, column and also the third dimension mostly as time. This review paper focuses on the triclustering approach followed in many kinds of data such as binary data, big data and most importantly in gene expression data. This work also divulges the computational overhead in dealing the three-dimensional data. It also provides a detailed view of the approaches followed in different triclustering algorithms, measures used, dataset applied and also the validation framework followed. Finally, it highlights challenges and opportunities to advance the field of triclustering and its applicability to complex three-dimensional data analysis.