With the demand for increasingly smaller feature sizes, extreme ultraviolet (EUV) lithography has become the cutting-edge technology for fabricating highly miniaturized integrated circuits. However, the limited brightness of the EUV light source, the distinct exposure mechanism, and the high resolution required for patterns pose significant challenges for resist materials—particularly for conventional polymeric resists, which often suffer from low EUV absorption, high molecular weight, and nonhomogeneous composition. In this review, we focus on polymer resists for EUV lithography and offer our perspectives on recent exciting advances in the polymer chemistry of these resists. For example, in recent years, there has been significant progress in incorporating high EUV-absorbing moieties and photosensitizers into resists to enhance EUV absorbance and quantum efficiency. In addition, advancements have been made in developing single-component chemically amplified resists (CARs) with covalently attached photoacid generators (PAGs), as well as main-chain scission-type resists. Furthermore, the creation of precision oligomeric resists with precisely defined primary sequences and discrete molecular weights has opened new possibilities for EUV resist design. Lastly, we provide a critical outlook on the future opportunities and challenges in the development of EUV resists.