We first review the role of sample eigenvalues in some classical methods of mul tivariate statistics, such as principal components and canonical correlation analysis.Results from random matrix theory can provide practically useful approximations when the ratio of the number of variables (p and q) to sample size n is not necessarily small.For concreteness, we focus on the limiting distribution for the largest prin cipal component variance and the largest canonical correlation in "null hypothesis" settings when the data matrices have independent standard Gaussian entries.