A heat pump water heater and systems and methods for its control. The systems are configured to heat water within a water storage tank of a heat pump water heater wherein a controller within the system is operatively connected to a plurality of heat sources including at least one electric heating element and a heat pump and sensors in order to selectively energize one of the plurality of heat sources. The controller is configure to process data representative of the temperature of water within the tank near the top of the water storage tank, and rate of water flowing out of the water storage tank, in order to automatically selectively energize the heat sources. The selection of heat sources by the controller is determined by a mode of operation selected by the user and the data processed by the controller in view of the selected mode of operation.