Extreme ultraviolet （EUV） normal-incidence optical systems are widely used in biological structure microscopic imaging， plasma diagnosis， solar physical observation， and EUV lithography. Therefore， these systems warrant further study. In this paper， the latest developments of the EUV normal-incidence optical system at the Institute of Precision Optical Engineering （IPOE） of Tongji University are presented. Several normal-incidence optical systems used in different applications， such as hot electrons diagnostics， micro-nano imaging， EUV radiation induced damage， and Z-pinch plasma diagnostics are listed. These systems have achieved excellent performance in their respective applications， achieving spatial resolutions of several microns at a millimeter scale field-of-view （FOV） and realizing ultrahigh spatial resolutions on the order of sub-microns for FOVs at tens of microns scale. The systems have also realized ultrahigh-energy-density EUV radiation through a focusing system with large a numerical aperture and helped perform spatiotemporal diagnostics with multi-energy and multi-channels. The research progress of the EUV normal-incidence optical system has provided strong support for the independent and controllable research of plasma diagnostic equipment and technological reserve of advanced manufacturing equipment in China.