Flow separation is the ejection of fluid particles from a small neighborhood of a solid boundary. Such a breakaway from the boundary is often due to the detachment of a boundary layer, but it also occurs in highly viscous flows where the boundary layer description is inapplicable. Accordingly, we will treat separation here as a purely kinematic phenomenon: the formation of a material spike from a flow boundary.Such material spikes form along attracting LCSs, as we have already seen inthe previous chapter. We consider LCSs acting as separation or attachment profiles here separately because their contact points with the boundary and their local shapes near the boundary can be located from a purely Eulerian analysis along the boundary. Since the attachment points of material separation profiles cannot move under no-slip boundary conditions, such profiles necessarily create fixed separation. In contrast, material spikes emanating from off-boundary points generally result in moving separation in unsteady flows. We will discuss how both fixed and moving separation can be described via material barriers to transport.