Intrinsically disordered proteins (IDPs), also known as intrinsically unstructured proteins (IUPs), lack a well-defined 3D structure in vitro and, in some cases, also in vivo. Here, we discuss the question of proteolytic sensitivity of IDPs, with a view to better explaining their in vivo characteristics. After an initial assessment of the status of IDPs in vivo, we briefly survey the intracellular proteolytic systems. Subsequently, we discuss the evidence for IDPs being inherently sensitive to proteolysis. Such sensitivity would not, however, result in enhanced degradation if the protease-sensitive sites were sequestered. Accordingly, IDP access to and degradation by the proteasome, the major proteolytic complex within eukaryotic cells, are discussed in detail. The emerging picture appears to be that IDPs are inherently sensitive to proteasomal degradation along the lines of the "degradation by default" model. However, available data sets of intracellular protein half-lives suggest that intrinsic disorder does not imply a significantly shorter half-life. We assess the power of available systemic half-life measurements, but also discuss possible mechanisms that could protect IDPs from intracellular degradation. Finally, we discuss the relevance of the proteolytic sensitivity of IDPs to their function and evolution.