Rocking ratchets are asymmetric potentials operated in the non-linear response regime where rectifying behaviour can be observed. Mesoscopic electronic devices based on semiconductors with low carrier concentration are easily driven away from linear response, and their electron dynamics is at low temperatures altered by quantum effects. Asymmetric semiconductor devices of sub-micron dimensions are therefore suitable for experiments on ``quantum ratchets'', that is, rocking ratchets based on quantum effects, such as electron interference and tunnelling. We first describe experiments using triangular electron cavities in the linear response regime, illustrating that, at low temperatures, classical and quantum electron dynamics are determined by the shape of the ballistic cavity. Physical reasons for a transition from linear to non-linear behaviour in mesoscopic devices are discussed, and two ratchet experiments in the non-linear regime are described. The sign of rectification in a quantum dot ratchet, based on electron interference effects, depends very sensitively on uncontrollably small deviations from the intended device shape, but can be tuned using parameters such as magnetic field, Fermi energy or the AC voltage. The current direction in a tunneling ratchet can be predicted from the device shape, and is tunable by temperature, when device parameters are suitably chosen.

PACS numbers: 73.23.Ad, 73.50.Fq, 73.40.Ei