Computing the eigenvalues and eigenvectors of a large matrix is a basic task in high dimensional data analysis with many applications in computer science and statistics. In practice, however, data is often perturbed by noise. In this talk, we will focus on the spiked covariance matrix model, a popular and sophisticated model proposed by Johnstone. We will present some recent results on the limiting behavior of the extreme eigenvalues and eigenvectors of the spiked covariance matrices in the supercritical case. This talk is based on joint work with Zhigang Bao, Xiucai Ding, and Jingming Wang.