A liquid handling robot for handling well plates. The robot has a powered anvil which loads pipette tips from a tray onto the cones of a liquid handling head by first clamping the liquid handling head to the anvil and then ramming a movable plate carrying the pipette tips onto the cones. The robot also allows for fully automated swapping between different heads, such as liquid handling heads or pin heads. A head parking station is provided for parking heads when they are not being used. The robot has an automated pipette tip tray dispenser based on storage cassettes that store vertically stacked pipette tip trays. The trays are dispensed one at a time out of the storage cassette past retaining catches which are normally inwardly positioned to carry the pipette tip trays, but are outwardly biasable by a dispensing mechanism to allow the lowest tray in the shaft to pass onto a conveyor which moves the tray to a pick-up position from which the head can move the tray to the powered anvil for pipette tip loading onto a liquid handling head.