Research in subspace and componentbased techniques were originated in Statistics in the middle of the last century through the problem of linear feature extraction solved by the Karhunen-Loève Transform (KLT). Then, it application to signal processing was initiated three decades ago, and has met considerable progress. Thorough studies have shown that the estimation and detection tasks in many signal processing and communications applications such as data compression, data filtering, parameter estimation, pattern recognition, and neural analysis can be significantly improved by using the subspace and componentbased methodology. Over the past few years new potential applications have emerged, and subspace and component methods have been adopted in several diverse new fields such as smart antennas, sensor arrays, multiuser detection, time delay estimation, image segmentation, speech enhancement, learning systems, magnetic resonance spectroscopy, and radar systems, to mention only a few examples. The interest in subspace and componentbased methods stems from the fact that they consist in splitting the observations into a set of desired and a set of disturbing components. They not only provide new insight into many such problems, but they also offer a good tradeoff between achieved performance and computational complexity. In most cases they can be considered to be lowcost alternatives to computationally intensive maximum-likelihood approaches