The classic structure-function paradigm has been challenged by a recently identified class of proteins: intrinsically disordered proteins (IDPs). Despite their lack of stable secondary or tertiary structure, IDPs are prevalent in all forms of life and perform myriad cellular functions, including signaling and regulation. Importantly, disruption of IDP homeostasis is associated with numerous human diseases, including cancer and neurodegeneration. Despite wide recognition of IDPs, the molecular mechanisms underlying their functions are not fully understood. Here we review the structural features and disorder-function relationships for p21 and p27, two cyclin-dependent kinase (Cdk) regulators involved in controlling cell division and fate. Studies of p21 bound to Cdk2/cyclin A revealed that a helix stretching mechanism mediates binding promiscuity. Further, investigations of Tyr88-phosphorylated p27 identified a signaling conduit that controls cell division and is disrupted in certain cancers. These mechanisms rely upon a balance between nascent structure in the free state, induced folding upon binding, and persistent flexibility within functional complexes. Although these disorder-function relationships are likely to be recapitulated in other IDPs, it is also likely that the vocabulary of their mechanisms is much more extensive than is currently understood. Further study of the physical properties of IDPs and elucidation of their links with function are needed to fully understand the mechanistic language of IDPs.