A hand operated pump for generating negative and positive air pressure. The pump includes a pump body having a pump cylinder and a piston mounted for reciprocation in the cylinder. A selector valve communicates with the cylinder and is moveable between a positive-pressure position and a negative-pressure position. The arrangement is such that operation of an actuator to move the piston through a power stroke when the selector valve is in its negative-pressure position causes the pump to generate negative pressure at an outlet of the pump, and operation of the actuator to move the piston through a power stroke when the selector valve is in its positive-pressure position causes the pump to generate positive pressure at the outlet of the pump. A method of operating such a pump is also disclosed.