As an unprecedented breakthrough in experimental molecular biology domain, DNA microarray enables simultaneously monitoring of the expression level of thousands of genes over many experimental conditions. Studies have shown that analyzing microarray data is essential for finding gene co-expression network, designing new types of drugs, preventing disease, and so on. To analyze gene expression datasets, the researchers design many clustering methods, which can only find fewer of useful knowledge. Due to a subset of genes co-regulate and co-express only under a subset of experimental conditions, and also not co-express at the same level, they can belong to several genetic pathways that are not apparent. In this situation, the biclustering method is proposed. At the same time, the direction of gene expression analysis changes from the whole pattern mining to the local pattern discovery, and then it changes the situation of clustering data only based on all the objects or attributes of the data. The paper introduces the state-of-the-art progress, which includes the definition of local pattern, the types and criteria of local pattern, mining and query methods of local pattern. Then it concludes the mining criteria based on quantity and quality, and related software. Further, it gives the problems in the existing algorithms and tools. Finally, we discuss the research direction in the future.