This article presents a comprehensive and critical review of slag entrainment in continuous casting molds. Entrainment is one of the main sources of inclusions in the final product, and so greatly harms clean steel production. By understanding the mechanisms that cause entrainment, the operating condition windows can be chosen to reduce defects. Nine mechanisms have been proposed over the last three decades, including top surface level fluctuations, meniscus freezing, vortexing, shear-layer instability, narrow face spout impingement upon the top surface, argon bubble interactions, slag crawling down the submerged entry nozzle (SEN), instability of the top-surface standing wave, and top surface "balding". Previous investigations into each of these mechanisms are summarized, including both quantitative and qualitative descriptions of behavior. The quantitative models are combined to suggest best practices for clean steel production, but more work is needed to improve these predictions.