This work is a technical review of past research and a synthesis of current understanding of post injections for soot reduction in diesel engines. A post injection, which is a short injection after a longer main injection, is an in-cylinder tool to reduce engine-out soot to meet pollutant emissions standards while maintaining efficiency, and potentially to reduce or eliminate exhaust aftertreatment. A sprawling literature on post injections documents the effects of post injections on engine-out soot with variations in many engine operational parameters. Explanations of how post injections lead to engine-out soot reduction vary and are sometimes inconsistent or contradictory, in part because supporting fundamental experimental or modeling data are often not available. In this paper, we review the available data describing the efficacy of post-injections and highlight several candidate in-cylinder mechanisms that may control their efficacy. We first discuss three in-cylinder mechanisms that have been frequently proposed to explain how post injections reduce engine-out soot. Thereafter, to provide a foundation for interpretation of past research, we briefly review basic soot formation and oxidation chemistry, and soot/fluid processes in fuel sprays and engine flows. Next, we provide a comprehensive overview of the literature on the efficacy of post-injections for soot reduction as a function of engine operational parameters including injection duration and dwell, exhaust-gas recirculation, load, boost, speed, swirl, and spray targeting. We conclude by identifying major remaining research questions that need to be addressed to help achieve a design-level understanding of the mechanisms of soot reduction by post injections.