In many situations, given a sequence of n random variables the covariance matrix is not know but has to be estimated. In the case we have m observations and m>>n then the sample covariance matrix is a good approximation of the true covariance. More specifically, for a fixed number of variables the sample covariance matrix converges with m to the true covariance. However, in applications like weather forecast, wireless communications (MIMO channels with a big number of antennas), linear estimation and military applications the number of observations is limited and usually one has m ≤ n. In this talk we will discuss what can be done in this scenario. This is based on a project done at Bell Labs with Tom Marzetta and Steve Simon where we used techniques from random matrices, free probability and representation theory.