In modern data analysis, the datasets are often represented by large-scale matrices or tensors (the generalization of matrices to higher dimensions). In this talk, I will talk about novel matrix/tensor decompositions, CUR decompositions, which are memory efficient and computationally cheap. Besides, I will also discuss the applications of CUR decompositions on developing efficient algorithms for robust decompositions. Additionally, some simulation results will be provided on real

and synthetic datasets.