Methods and systems for endovascular, endocardiac, or endoluminal approaches to a patient's heart to perform surgical procedures that may be performed or used without requiring extracorporeal cardiopulmonary bypass. Furthermore, these procedures can be performed through a relatively small number of small incisions. These procedures may illustratively include heart valve implantation, heart valve repair, resection of a diseased heart valve, replacement of a heart valve, repair of a ventricular aneurysm, repair of an arrhythmia, repair of an aortic dissection, etc. Such minimally invasive procedures are preferably performed transapically (i.e., through the heart muscle at its left or right ventricular apex).