A high pressure pump for use in the injection of liquid chemicals into subsea oil or gas wells, and intended to be positioned in the subsea environment adjacent to the wellhead, comprises a piezoelectric actuator (19) for reciprocating a plunger (22) which acts to compress and expand the effective volume of a pumping chamber (29) having a valved inlet (15) connected to a source of the liquid and a valved outlet (16) to lead the liquid to the well. The device has a minimum of moving parts and in particular avoids the need for any rotating parts and attendant high performance bearings and seals.