Abstract: Nonlinear eddy viscosity and algebraic stress models are currently providingan invaluable link between the more common linear eddy viscosity turbulencemodels and the full differential Reynolds stress forms. With the increasedpopularity has come an abundance of different formulations. The purpose ofthis review is to provide a cohesive framework for the variety of modelsproposed and to highlight the various similarities and differences among themodels. Their link with differential Reynolds stress models and theirimproved predictive capability over linear eddy-viscosity models is alsohighlighted.