In this chapter we provide a detailed description of a source reconstruction approach, beamforming, which was only recently introduced to electroencephalography (EEG) and magnetoencephalography (MEG) (Robinson and Vrba, 1999; van Veen el al., 1997). As with any other source reconstruction method, a set of a prim, assumptions are made so that a solution to the inverse problem can be obtained (e.g., Baillet et al., 2001). The main assumption behind the beamformer approach is that no two distant cortical areas generate coherent local field potentials over long time scales; it has been shown empirically (Hillebrand el al., 2005; Singh el al., 2002) that this is a reasonable assumption set. We argue on the basis of anatomical and electrophysiological data why the beamformer assumption set, although simplistic, may indeed be quite plausible. We also illustrate when the assumptions might fail and make suggestions for improvements in the beamformer implementations. We conclude that beamforming is an exciting new approach to MEG source reconstruction that could provide another stepping stone on the route towards an appropriate assumption set with which to non-invasively image the brain.