Methods based on single-molecule localization and photophysics have brought nanoscale imaging with visible light into reach. This has enabled single-particle tracking applications for studying the dynamics of molecules and nanoparticles and contributed to the recent revolution in super-resolution localization microscopy techniques. Crucial to the optimization of such methods are the precision and accuracy with which single fluorophores and nanoparticles can be localized. We present a lucid synthesis of the developments on this localization precision and accuracy and their practical implications in order to guide the increasing number of researchers using single-particle tracking and super-resolution localization microscopy.