Extreme ultraviolet lithography (EUVL) is the leading technology for enabling miniaturization of computational components over the next decade. Next-generation resists will need to meet demanding performance criteria of 10 nm critical dimension, 1.2 nm line-edge roughness, and 20 mJ cm(-2) exposure dose. Here, the current state of the development of EUV resist materials is reviewed. First, pattern formation in resist materials is described and the Hansen solubility sphere (HSS) is used as a framework for understanding the pattern-development process. Then, recent progress in EUVL resist chemistry and characterization is discussed. Incremental advances are obtained by transferring chemically amplified resist materials developed for 193 nm lithography to EUV wavelengths. Significant advances will result from synthesizing high-absorbance resist materials using heavier atoms. In the framework of the HSS model, these materials have significant room for improvement and thus offer great promise as high-performance EUV resists for patterning of sub-10 nm features.