This paper summarizes the mathematical surface equations which are useful in two-phase flows and single-phase reacting flows. The connection between the interfacial area concentration transport equation for two-phase flows and the flame surface density transport equation for turbulent reacting flows is established. Several analytical examples are given to clarify the physical significance of the different quantities involved in the different transport equations. An introduction to the mathematical treatment of anisotropic interfaces is also given. This theory is illustrated on two different numerical examples: a single inclusion in a simple shear and a single inclusion in an uni-axial elongation. (c) 2007 Elsevier Ltd. All rights reserved.