Clustering and biclustering are important techniques arising in data mining. Different from clustering, biclustering simultaneously groups the objects and features according their expression levels. In this review, the backgrounds, motivation, data input, objective tasks, and history of data biclustering are carefully studied. The bicluster types and biclustering structures of data matrix are defined mathematically.Most recent algorithms, including OREO, nsNMF, BBC, cMonkey, etc., are reviewed with formal mathematical models. Additionally, a match score between biclusters is defined to compare algorithms. The application of biclustering in computational neuroscience is also reviewed in this chapter.