In this paper, we formulate the multi-pitch estimation problem and propose a number of methods to estimate the set of fundamental frequencies. The proposed methods, based on the nonlinear least-squares (NLS), MUltiple SIgnal Classification (MUSIC) and the Capon principles, estimate the multiple fundamental frequencies via a number of one-dimensional searches. We also propose an iterative method based on the Expectation Maximization (EM) algorithm. The statistical properties of the methods are evaluated via Monte Carlo simulations for both the single- and multi-pitch cases.