<p>The free-surface vortex is a rotational flow phenomenon characterized by two-phase coupling, formed by the rupture of surface fluid in the final stage of discharge. It is a significant concept with broad applications in engineering fields like metallurgy and hydraulics. The basic concepts and characteristics of free-surface vortices were introduced, and their hazards in various fields were discussed. The development of theoretical and numerical models over recent decades was reviewed, and the factors affecting vortex formation and existing suppression methods were outlined. Finally, the key challenges and focus areas on the study of free-surface vortex were summarized. With the ongoing advancements in computational fluid dynamics and experimental technology, research on free-surface vortices will become more in depth and precise. Additionally, interdisciplinary cooperation and technological innovation are expected to achieve precise control and optimal design of free-surface vortices, offering more efficient and sustainable solutions for metallurgy and related engineering fields.</p>