Over the last 10-15 years, there has been renewed interest in understanding various probabilistic properties of large random matrices. These objects also come up naturally in high-dimensional statistics problems. In this talk, I will describe some of the light random matrix results shed on various classical and modern problems in multivariate statistics, discuss robustness issues (and lack thereof) of random matrix models and present some consequences for problems in optimization, classification, and time permitting, numerical linear algebra.