Methods and systems for minimally invasive replacement of a valve. The system includes a collapsible valve and anchoring structure, devices and methods for expanding the valve anchoring structure, adhesive means to seal the valve to the surrounding tissue, a catheter-based valve sizing and delivery system, native valve removal means, and a temporary valve and filter assembly to facilitate removal of debris material. The valve assembly comprises a valve and anchoring structure for the valve, dimensioned to fit substantially within the valve sinus.