Research of a past decade and a half leaves no doubt that complete understanding of protein functionality requires close consideration of the fact that many functional proteins do not have well-folded structures. These intrinsically disordered proteins (IDPs) and proteins with intrinsically disordered protein regions (IDPRs) are highly abundant in nature and play a number of crucial roles in a living cell. Their functions, which are typically associated with a wide range of intermolecular interactions where IDPs possess remarkable binding promiscuity, complement functional repertoire of ordered proteins. All this requires a close attention to the peculiarities of biophysics of these proteins. In this review, some key biophysical features of IDPs are covered. In addition to the peculiar sequence characteristics of IDPs these biophysical features include sequential, structural, and spatiotemporal heterogeneity of IDPs; their rough and relatively flat energy landscapes; their ability to undergo both induced folding and induced unfolding; the ability to interact specifically with structurally unrelated partners; the ability to gain different structures at binding to different partners; and the ability to keep essential amount of disorder even in the bound form. IDPs are also characterized by the "turned-out" response to the changes in their environment, where they gain some structure under conditions resulting in denaturation or even unfolding of ordered proteins. It is proposed that the heterogeneous spatiotemporal structure of IDPs/IDPRs can be described as a set of foldons, inducible foldons, semi-foldons, non-foldons, and unfoldons. They may lose their function when folded, and activation of some IDPs is associated with the awaking of the dormant disorder. It is possible that IDPs represent the "edge of chaos" systems which operate in a region between order and complete randomness or chaos, where the complexity is maximal. This article is part of a Special Issue entitled: The emerging dynamic view of proteins: Protein plasticity in allostery, evolution and self-assembly.