In the context of gene expression microarray data, biclustering is a technique to identify clusters of genes that are co-expressed under clusters of conditions. It usually has high computational complexity (NP-Hard). In computer science domain, combinatorial problems like biclustering, refer to the tasks associated with the discovery of grouping, ordering or assigning a discrete set of objects fulfilling some fixed constraints. Greedy Search approach is a popular method often used for solving combinatorial problems. It is adoptable in this context because of its variety aspects of search performance. Its variability caused by randomization and the robustness in parameter settings improves the search performance. This review article presents a brief survey of various greedy based biclustering algorithms that are being frequently applied on gene expression microarray data. These algorithms are further classified into iterative greedy approach and stochastic greedy approach based on their search criteria.