Introduction. Non-Stratified Ambient Currents: Shallow-Water (SW) Formulation for High-Re Flows. The Steady-State Current and Nose Jump Conditions. Box Models for 2D Geometry. Two-Layer SW Model. Axisymmetric Currents, SW Formulation. Box Models for Axisymmetric Geometry. Effects of Rotation. Buoyancy Decays: Particle-Driven, Porous Boundary, And Entrainment. Non-Boussinesq Systems. Lubrication Theory Formulation for Viscous Currents. Stratified Ambient Currents and Intrusions: Continuous Density Transition. Axisymmetric and Rotating Cases. The Steady-State Current. Intrusions in 2D Geometry. Intrusions in Axisymmetric Geometry. Box Models for 2D Geometry. Box Models for Axisymmetric Geometry. Lubrication Theory for Viscous Currents with S = 1. Energy.