We consider the equilibrium behaviour and dynamics of liquid drops on a superhydrophobic surface patterned with sawtooth ridges or posts. Due to the anisotropic geometry of the surface patterning, the contact line can preferentially depin from one side of the ratchets, leading to a novel, partially suspended, superhydrophobic state. In both this configuration, and the collapsed state, the drops show strong directional contact angle hysteresis as they are pushed across the surface. The easy direction is, however, different for the two states. This observation allows us to interpret recent experiments describing the motion of water drops on butterfly wings.