Disclosed is a substrate support for an apparatus of the type which projects a beam of EUV radiation onto a target portion of a substrate (400). The substrate support comprises a substrate table constructed to hold the substrate, a support block (420) for supporting the substrate table, and a cover plate (450′) disposed around the substrate table. The top surface of the cover plate and the top surface of a substrate mounted on the substrate table are all substantially at the same level. At least one sensor unit (430) is located on the substrate support and its top surface is also at the same level as that of the cover plate and substrate. Also disclosed is an EUV lithographic apparatus comprising such a substrate support.