CUR decomposition is a low-rank matrix decomposition that is formed using a small number of actual columns and actual rows of the data matrix. Since this decomposition is explicitly constructed using entries from the actual data set, CUR decomposition may be interpretable by practitioners; for this reason, it is sometimes preferable to the Singular Value Decomposition. I will explain various deterministic and randomized algorithms for computing the CUR decomposition and methods to analyze its accuracy. I will also explain how CUR decomposition can be applied to areas such as recommendation systems, facial recognition and handwriting digit classification.