The talk will consist in two parts. The first part will be an overview of SLEPc, the Scalable Library for Eigenvalue Problem Computations. SLEPc is a software library for finding a few eigenvalues and eigenvectors of large, sparse matrices in parallel computers. It provides implementations of different iterative methods such as Lanczos (for symmetric problems) and Arnoldi (for non-symmetric problems). In the second part of the talk, the emphasis will be placed on how to implement these method in parallel so that they can scale well up to hundreds of processors. We will illustrate several techniques that have been successfully implemented in SLEPc, including performance results.