Nanoscale imaging of biological samples can provide rich morphological and mechanistic information about biological functions and dysfunctions at the subcellular and molecular level. Expansion microscopy (ExM) is a recently developed nanoscale fluorescence imaging method that takes advantage of physical enlargement of biological samples. In ExM, preserved cells and tissues are embedded in a swellable hydrogel, to which the molecules and fluorescent tags in the samples are anchored. When the hydrogel swells several-fold, the effective resolution of the sample images can be improved accordingly via physical separation of the retained molecules and fluorescent tags. In this review, we focus on the early conception and development of ExM from a biochemical and materials perspective. We first examine the general workflow as well as the numerous variations of ExM developed to retain and visualize a broad range of biomolecules, such as proteins, nucleic acids, and membranous structures. We then describe a number of inherent challenges facing ExM, including those associated with expansion isotropy and labeling density, as well as the ongoing effort to address these limitations. Finally, we discuss the prospect and possibility of pushing the resolution and accuracy of ExM to the single-molecule scale and beyond.