Methods and devices are provided for improving cardiac output. The methods involve establishing a fluid communication pathway between the left ventricle and another natural or prosthetic structure. In one method, a conduit is implanted between the left ventricle and the descending aorta where ventricular blood flows from the left ventricle directly into the descending aorta and bypassing the aortic valve. The devices include such conduits and valves for forming the fluid communication pathways.