The field of light-scattering characterization of single particles has seen a rapid growth over the last 30 years largely due to the progress in measurement and simulation capabilities. In particular, several methods have been developed to reliably characterize various particles, described by a model with several characteristics, with geometric resolution significantly better than the diffraction limit. However, their development has been largely fragmentary, limited to specific experimental set-ups. To fill this gap, these lines of development are reviewed within a unified framework. While focusing on characterization algorithms themselves, the experimental aspects related to the isolation and measurement of single particles are also discussed. The existing characterization methods are divided into three classes. The widest class is that of model-driven methods based on solving parametric inverse light-scattering problems, using a direct inversion of a low-dimensional mapping, a nonlinear regression, or neural networks. Other classes include model-free reconstruction methods and data-driven classification methods. This review is designed to be extensive in including all relevant literature, but the discussion of semi-quantitative imaging methods, such as tomography or holography-based reconstruction, is deliberately omitted. Throughout the review the development of various characterization methods is described, they are critically compared, and promising directions of future research are highlighted.