Proteins are dynamic creatures. Intrinsically disordered proteins (IDPs) function as multiplicity of structures and their activities can only be described by stochastic structure-function relationships. In their complex forms, however, IDPs were thought to lose their plasticity and behave similarly to globular proteins. Although various IDPs indeed fold upon binding, this view is not valid in general. IDPs usually interact with their partners via short motifs, which require malleable environments to function. Consequently, segments of IDPs could retain their disordered state in the complex, a phenomenon termed as fuzziness. Since its recognition, the number of structurally characterized fuzzy complexes, both with protein and DNA, rapidly increases. Here I review recent advances in our understanding of fuzziness. Four basic mechanisms are described how conformationally heterogeneous regions impact specificity or binding affinity of protein complexes. A novel allostery-model is proposed, where the regulatory site modulates the conformational equilibrium of the binding interface without adopting a unique structure. Protein-protein interactions, post-translational modifications or alternative splicing of the highly flexible/disordered regions offer further opportunities for regulation and expand the functional repertoire of fuzzy complexes.