Matrix Computations are ubiquitous in all areas of science and engineering. In this talk, I will first survey some traditional problems in matrix computations and discuss issues that arise in solving them, such as, accuracy, algorithms and software. Then, I will discuss various matrix computation problems that arise in machine learning, especially specialized computations, such as non-negative matrix factorization, multilevel graph clustering and kernel learning. I will conclude with a pointer to resources and a discussion.