The verification of the structural components of demonstration fusion power plants requires design criteria developed specifically for those components and the unique conditions at which they are operated. Therefore the creation of a body of structural design criteria appropriate for demonstration fusion power plants is an important activity, with particular attention required for the in-vessel components of the divertor and blanket. For posited failure modes associated with the candidate in-vessel components for the current European Demonstration Power Plant design (EU DEMO), this paper highlights the gaps identified in the leading suites of relevant structural design criteria (ASME BPVC Division III, AFCEN RCC-MRx, ITER SDC-IC). Opportunities for innovative development are then explored for these gaps. Finally, a development path for structural design criteria against the needs of EU DEMO is discussed.