In this paper, we review the signatures of a new elastic phase that is found in glasses with selected compositions. It is shown that in contrast with random networks, where rigidity percolates at a single threshold, networks that are able to self-organize to avoid stress will remain in an almost stress-free state during a compositional interval, a Boolchand intermediate phase, that is bounded by a flexible phase and a stressed rigid phase. We report the experimental signatures and describe the theoretical efforts that have been accomplished to characterize the Boolchand intermediate phase. We illustrate one of the methods used in more detail with the example of Group III chalcogenides and finally suggest further possible experimental signatures of self-organization.