Disordered states of proteins include (i) the unfolded states of folded proteins and (ii) the biologically functional intrinsically disordered proteins. Due to the highly dynamic and conformationally heterogeneous nature of disordered states, traditional methods for structural characterization are not directly applicable. Nevertheless, recent years have brought major advances in the experimental characterization of disordered states. In particular, multidimensional NMR methods have proven extremely valuable for improving our understanding of these highly flexible systems. Extensive experimental evidence now supports the idea that disordered states under non-denaturing or mildly denaturing conditions have interesting structural properties that deviate substantially from the random coil-like behavior observed for chemically denatured proteins. In this chapter, we review various experimental techniques for characterizing non-random secondary and tertiary structure in disordered states of proteins. In addition, we discuss recent attempts at combining experimental measurements with computational methods in order to build detailed atomic-level models of various unfolded and intrinsically disordered proteins.