Holographic techniques are indispensable tools for modern optical engineering. Over the past two decades, research about incoherent digital holography has continued to attract attention. Optical scanning holography (OSH) can obtain incoherent holograms using single-pixel detection and structured illumination with Fresnel zone patterns (FZPs). Particularly by changing the size of a detector, OSH can also obtain holograms under coherently illuminated conditions. Since 1979, OSH has continuously evolved. According to the evolution of semiconductor technology, spatial light modulators (SLMs) come to be useful for various imaging fields. By using SLM techniques for OSH, the practicality of OSH is improved. These SLM-based OSH methods are termed computational OSH (COSH). In this review, the configurations, recording and reconstruction methods, and proposed applications of COSH are reviewed.