Random matrix theory in the non-asymptotic regime, for high but fixed dimensions, has experienced a surge of new methods and results in the last decade. We will review some of these methods, focusing on extreme singular values. Applications will be given to covariance estimation problem - how many samples (n) does one need in order to estimate the covariance matrix in dimension p? Both regimes n>p and n<p are important, but our understanding of either of them is not complete.