We review single-molecule localization microscopy techniques with a focus on computational techniques and algorithms necessary for their use. The most common approach to single-molecule localization, Gaussian fitting at positions pre-estimated from local maxima, is illustrated in depth and techniques for two- and three-dimensional data analysis are highlighted. After an introduction explaining the principle requirements of single-molecule localization microscopy, we discuss and contrast novel approaches such as maximum likelihood estimation and model-less fitting. Finally, we give an overview over the existing, scientifically available software and show how these techniques can be combined to quickly and easily obtain super-resolution images.