Non-uniformity plays an important role for MHD waves. For a uniform plasma of infinite extent the MHD waves can be subdivided in two classes with distinct properties. The first class contains the Alfvén waves. The Alfvén waves are incompressible and propagate parallel vorticity. They do not have a parallel component of displacement, they do not cause variations in pressure and are driven by magnetic tension only. The second class contains the magneto-sonic waves. They are compressible and have a parallel component of displacement. They do not propagate parallel vorticity and are driven by pressure and magnetic tension. In non-uniform plasmas the situation can be very different. The clear division between Alfvén waves and magneto-sonic waves is no longer present. In a given part of the equilibrium an MHD wave can strongly resemble a magneto-sonic wave with little or no resemblance to Alfvén waves; while in another part of the equilibrium the MHD wave is practically an Alfvén wave, which has the amazing property of being accompanied by variations in pressure.