Single-molecule localization microscopy (SMLM) generates super-resolution images by serially detecting individual fluorescent molecules. The power of SMLM, however, goes beyond images: biologically relevant information can be extracted from the mathematical relationships between the positions of the fluorophores in space and time. Here we review the history of SMLM and how recent progress in methods for spatial point analysis has enabled quantitative measurement of SMLM data, providing insights into biomolecule patterning, clustering and oligomerization in biological systems.