The European DEMO power reactor is currently under conceptual design within the EUROfusion Consortium. One of the most critical activities is the engineering of the plasma-facing components (PFCs) covering the plasma chamber wall, which must operate reliably in an extreme environment of neutron irradiation and surface heat and particle flux, while also allowing sufficient neutron transmission to the tritium breeding blankets. A systems approach using advanced numerical analysis is vital to realising viable solutions for these first wall and divertor PFCs. Here, we present the system requirements and describe bespoke thermo-mechanical and thermo-hydraulic assessment procedures which have been used as tools for design. The current first wall and divertor designs are overviewed along with supporting analyses. The PFC solutions employed will necessarily vary around the wall, depending on local conditions, and must be designed in an integrated manner by analysis and physical testing.