Spontaneous motion of liquid droplets can occur on hydrophobic, micro-structured, solid surfaces comprising a structural gradient. In this study, we examine such motion experimentally and explain our observations by invoking variable droplet–surface interactions (both actuation and resistance forces) arising from the structural gradient. The oscillatory motion of the droplet constitutes an integral aspect of the behaviour and this is incorporated into the overall modelling. The theoretical model features a truncated spheroid for the drop shape (flattened in the region of solid contact) coupled with the oscillatory and alternate leading and trailing motion of the contact line. Results from the model and experiments provide good qualitative and quantitative agreement. The component of the vertical oscillation is found to help overcome wetting hysteresis and actuate the motion, this being a key element for the completeness of the model.