Methodology and related medical devices for effectively bypassing a blocked or partially blocked coronary artery and providing oxygenated blood to the myocardium. A coronary artery bypass method utilizes a shunt member. An upstream end portion of the shunt member is disposed in the myocardium of a patient's heart so that the upstream end portion communicates with the left ventricle of the patient's heart. An opposite or downstream end portion of the shunt member is placed in communication with a coronary artery of the patient downstream of a blockage in the coronary artery. The shunt member extends into the coronary artery from the myocardium either directly or indirectly with an intermediate or middle portion of the shunt member being disposed in an intrapericardial space of the patient, outside of the myocardium and outside of the coronary artery. In a method for performing a myocardial revascularization a passageway is formed at least partially through a myocardium of a patient from an outer surface of the patient's heart, with a surgical operation being performed at an outer end of the passageway to permanently close the passageway at the outer end. The passageway may extend though a posterior wall of a coronary artery and is produced by forming an aperture in an anterior wall of the coronary artery and forming the passageway in substantial alignment with the aperture. The closure of the passageway is effectuated particularly by closing the aperture in the anterior wall of the coronary artery.