Past theoretical work has shown that for low-frequency flow at a given ocean boundary location, a critical frequency ωc exists such that for ω>ωc unforced motion is trapped to the coast while for ω<ωc energy leaves the coast. Alternatively, for motion of a given frequency ω on the boundary, there exists a critical latitude such that the motion is trapped to the coast poleward of the latitude but equatorward it is not. This theory is discussed physically for both meridional and nonmeridional boundaries. The simple formula for critical frequency along a nomeridional boundary is used to document critical periods for the eastern and western Atlantic, Pacific, and Indian Ocean boundaries. The theory occasionally breaks down when boundary curvature is too large.