A gravity current consists of the flow of one fluid within another when this flow takes place because of relatively small differences in density between the fluids. A turbidity current is a gravity current where the density difference is produced principally by solid particles suspended in the current by fluid turbulence although compositional differences may also contribute to the density difference. Turbidity currents enter into a vast array of geophysical and engineering applications and their theoretical description has been based principally upon the hydrostatic(hydraulic) assumption that leads to classical shallow-water theory with some additions to account for the presence of particles. Here we will examine the origins and manifestations of nonhydraulic effects in models of turbidity currents.