A disposable fluid pump is provided with a housing including first and second faces, with a sidewall extending between the first and second faces. The housing defines a chamber, with an inlet and an outlet in fluid communication with the chamber. An impeller is rotatably mounted within the chamber and includes a plurality of flexible vanes. Such a pump may be incorporated into a disposable fluid flow circuit that is adapted to be mounted on a durable hardware for processing a fluid. In such a fluid flow circuit, the fluid pump may be integrated into a cassette of the circuit or, alternatively, the inlet and outlet of the fluid pump may be directly connected to fluid flow conduits of the circuit.