Oil spreading is one of the major factors affecting the fate of oil spills on water. Modeling spreading is required to study the impact of oil slicks on the environment and plants using sea water including desalination units. Spreading of oil on water undergoes three stages. In the second stage, gravity acts
as the main driving force against the viscous force, which is the main resisting force in stages 2 and 3. The paper presents the state of the art in modeling the second stage of spreading. Challenges in analyzing viscous-gravity spreading of continuously discharged oil on water are also presented.