We present a mathematical description of turbulent entrainment that is applicable to free-shear problems that evolve in space, time or both. Defining the global entrainment velocity V¯g to be the fluid motion across an isosurface of an averaged scalar, we find that for a slender flow, V¯g=u¯ζ−D¯ht/D¯t, where D¯/D¯t is the material derivative of the average flow field and u¯ζ is the average velocity perpendicular to the flow direction across the interface located at ζ=ht. The description is shown to reproduce well-known results for the axisymmetric jet, the planar wake and the temporal jet, and provides a clear link between the local (small scale) and global (integral) descriptions of turbulent entrainment. Application to unsteady jets/plumes demonstrates that, under unsteady conditions, the entrainment coefficient α no longer only captures entrainment of ambient fluid, but also time-dependency effects due to the loss of self-similarity.